While you might not have thought of Las Cruces as a place to live, it is certainly worth investigating. This is not what you'd expect in the desert. Sitting at 3,900 feet elevation, Las Cruces is surrounded by mountains and has the Rio Grande river just west of the downtown area. But why we'd like to retire in Las Cruces, New Mexico is it's laid back culture, the arts scene, the weather and the outdoor opportunities. Often mentioned in the lists of "Best Places to Retire", AARP listed Las Cruces as one of it's "Dream Towns" for retirement.
The New Mexico State University has it's main campus here. An agricultural college, it has 18,500 students and is also home to the NASA Space Grant Program.
About 100,000 people live here and 14% are over the age of 65. The median home listing price is $177,000 and rentals run in the $850 range. This makes it pretty affordable to have a snowbird retreat! We found this great newer home, 3 bedrooms and two baths with all appliances for $127,000.
There is a lot to see and do in Las Cruces! The town has fine art galleries, several live performance theatres, and some great restaurants with fabulous Mexican food. The White Sands Military Base is really interesting for all ages and has an informative museum. The Old Mesilla Village downtown is just charming. If you are a hiker, head up to Soledad Canyon to see the caves and pools. Be sure to bring water and wear good hiking shoes. And bring your camera for the view.
Las Cruces is home to several medical facilities who offer a wide range of specialties. There is also a larger airport just outside town.
But what about the weather? Not bad. Winter daytime temperatures range in the 50's and 60's. Fall and spring can get into the 70-80 degree range. Summers often reach 95! They only get about 10 inches of rain each year.
There is a very nice retirement community nearby, Pueblos at Alameda Ranch. We drove through and saw some of the beautiful new homes (in the $250,000 range) and the facilities including pools, clubhouse, etc.
With world class Mexican food, year-round golf, historic attractions and festivals, and 320 days of sunshine a year, what's not to love!


text:
Royaume-Uni >
Nom: Occupational Pension Schemes (Deficiency on Winding Up etc.) Regulations 1992 (S.I. No. 1555 of 1992)
Sujet(s): Prestations de vieillesse, d'invalidité et de survivants; Sécurité sociale (Normes d'ensemble)
Publié le: Printed separately, 3 p.
ISN: GBR-1992-R-29986
Bibliographie: Printed separately, 3 p.
Résumé/Citation: Provides for the calculation of the scheme's liabilities and assets and modify the application of section 58B in relation to the schemes which apply to earners in employment under different employers, and to schemes in respect of which there are no members in pensionable service.
Texte(s) de base:
1975-08-07 (GBR-1975-L-18673)Social Security Pensions Act 1975 (Chapter 60)
1975-03-20 (GBR-1975-L-18659)Social Security Act 1975 (Chapter 14)
Texte(s) abrogateur(s):
1994-03-23 (GBR-1994-R-36550)Occupational Pension Schemes (Deficiency on Winding Up etc.) Regulations 1994 (S.I. No. 895 of 1994)

redpajama_set_name: RedPajamaCommonCrawl


ARGuing for Multilingual Motivation in Web 2.0 is a European Union education project for motivating secondary school students to learn languages.
In my prior posting ARGuing: Serious Games in Education, I provided an overview for the project that consists of an Alternate Reality Game (ARG), which works as a communication context for international, multilingual, peer student communities that have to solve a puzzle by working as a multiplayer collaborative group in multiple languages.
The project team has also learnt how an ARG can be adapted to almost any area of education.
The ARG The Tower of Babel embeds a story designed to engage the target group: students are to save the planet by completing specific quests, collaboratively and internationally.
The game has enrolled 400+ teachers and students from 17 countries, with more than 9,000 quests answered and 800 files uploaded.
e. Papers' summary on pedagogy, evaluation and technology employed.
The project team is also offering consulting services to other educators interested in using ARGs in education.
For further details please contact Prof. Thomas Connolly, Coordinator ARGuing EU Project, University of The West of Scotland.


Participating in event marketing can be a pretty big deal, whether you're joining an event as an exhibitor or putting on an event of your own. It requires time, resources, and often a substantial budget. But according to the EventTrack 2015 survey, most marketers consider the investment worthwhile. In fact, 48 percent of brands realize ROI between 3:1 and 5:1, and 29 percent report a 10:1 return on their event marketing investments.
So how can you get the maximum return on your event? Use event-based content to build major marketing momentum.
Aside from all the in-person customer connections, events create another valuable asset: content—and lots of it. That is, of course, if you're taking advantage of the opportunities to create it.
An event provides a rich, loamy soil from which to sprout all kinds of highly engaging content. This content provides value in two fundamental ways.
Expanding the relationship with attendees: Content resulting from a live event can extend and enrich all those in-person customer connections and positive perceptions by keeping the relationship going. For example, following up with attendees of a session by providing a downloadable PowerPoint is a good way of reinforcing what they learned during the presentation, and it reminds them to follow up with your brand. It also gives them something to share.
Engaging people who didn't attend: You can use your event-based content to build relationships with people even if they weren't present at your event. Not only do non-attendees get a rich selection of authentic content to consume, but they also get a taste of what they're missing by not attending the event. They might even be compelled to invest in a conference pass next time.
You can use a mix of content strategies to get the most from event marketing. Remember to go beyond simply announcing your involvement with an event—offer something substantive. Below are some starting points.
Video, video, video: Think interviews, demos, and time lapses. And with platforms like Vine and Periscope, your video doesn't necessarily have to be polished and high grade. User-generated content is fair game. Video is a popular medium—it's engaging, and it's shareable. It's a win, win, win.
Enrich with commentary: Create a newsletter article or blog post that expands on a topic related to your presence at the show. Tease a presentation by introducing a discussion on topics that will be covered, or follow up on a presentation by going beyond what was shared. Or, summarize the presentation and include a link to an instant replay so people who didn't attend the event can benefit from the information.
Promote before, during, and after: Remind your audience, both the in-person attendees as well as your digital audience, of what you're offering at the show. Build anticipation by promoting beforehand, rise above the noise by promoting during, and follow up by promoting after. Social media is usually the best vehicle, but remember to keep your promotions substantive and focused on the value of the information you're offering. For more information, check out our post on how to promote your trade show presence with social media.
Employ lead gen strategies: Collect the contact information of booth visitors and/or presentation attendees (with their knowledge, of course) and follow up with targeted, relevant content. Or, take some of the rich, substantive content you created from the event, an in-depth interview perhaps, and gate it behind a lead gen form. Just make sure that you're offering enough to make it worthwhile.
Extending the value of your event marketing with content requires strategy and planning. But if done right, you'll likely experience spillover of the ROI created from the event itself. Just make sure your event content is relevant and provides value to your audience so that you maintain the positive brand perceptions you created.


text:
\section{Introduction}

The market risk premium is one of the main factors that drives the return of
any given portfolio of assets. Hence it is a key quantity for hedge funds, pension
funds, and numerous other investors. The risk premium can make investments
grow smoothly or jump up and down widely, often in an unpredictable manner.
In spite of its importance in asset allocation, however, the risk premium is
notoriously difficult to estimate from observed price processes of various risky
assets (see, e.g., Rogers 2001). Is it possible then to estimate the risk premium
from current prices of financial derivatives?

If $\{S_t\}$ denotes the price process of a risky asset and $h(s)$ is the payout
function of a European contingent claim expiring at $T$, then the price of this
derivative is given by the expectation of the cash flow $h(S_T)$, suitably
discounted, in the risk-neutral measure. Because asset price processes in
the risk-neutral measure are independent of the market risk premium, one
might be tempted to conclude therefore that derivative prices are likewise
independent of the risk premium. Indeed, in the case of the
Black-Scholes-Merton model where all relevant parameters are constant in
time, the risk premium parameter essentially drops out of various derivative
pricing formulae. Notwithstanding this example, it is worth bearing in mind that
the choice of the pricing measure does depend on the choice of the risk
premium. Thus, derivative prices in general will depend implicitly on the risk
premium, often in a nonlinear way. It follows that calibration of the market
risk premium from option prices is feasible within a given modelling framework
(Brody \textit{et al}. 2011).

The main purpose of the present paper is to address the question whether it is
possible, at least in principle, to determine the risk premium unambiguously, if
the totality of arbitrage-free market prices for various derivatives were available.
We shall find that the market risk premium consists of two components in an
additive manner (for models based on Brownian filtrations): The first of
the two, which we might call a `systematic' component, depends explicitly on
the term structure of the market, while the second, which we might call an
`idiosyncratic' component, is independent of the term structure of the market,
and thus can be identified as \textit{pure noise}. We show that the systematic
component can in principle be determined from current market data, whereas
the idiosyncratic noise component is strictly `hidden' and thus cannot be
inferred from derivative prices. Therefore, the risk premium can be backed
out from market data only up to an indeterminable additive noise.

Although the noise component cannot be inferred directly, it nevertheless has
an impact on the dynamics of asset prices under the physical measure, even
though it does not reflect the `true' state of affairs. Hence a spontaneous creation
of superfluous noise can move the price of an asset in an essentially arbitrary
direction. In particular, because the risk premium, and hence its noise component,
is a vectorial quantity, the direction of the noise vector can at times lie close to
the directions of volatility vectors of the share prices of a particular industrial sector,
leading to the creation of a `bubble' for that sector by pushing up those share
prices. When a more reliable information concerning the state of that sector is
unveiled, the direction of the risk premium vector is likely to change so as to
generate a negative component in the excess rate of return. This can be
exacerbated by an increase in the magnitude of asset volatilities due to
information revelation,
thus leading to a `burst'. Such a scenario need not be confined to a particular
financial sector; the existence of the so-called `equity premium puzzle' over a
specified period can likewise be attributed to the prevailing noise that points in
the general direction of the equity market volatility, but not in the direction of the
bond market volatility.

Needless to say, our formulation does not explain the cause of the creation
of anomalous price movements such as a financial bubble or an equity premium;
nor does it address the predictability of these events. In fact, according to our
characterisation, bubbles can at best be identified retrospectively, after their
bursts. Nevertheless, we are able to describe the mechanism by which such
anomalous price movements are generated in a simple and intuitive manner. In
particular, since our characterisation of a bubble is different from those more
commonly used in the literature, we are able to circumvent the analysis based on
subtle distinctions between local and true martingales. We also provide a heuristic
argument why the hidden noise might have the tendency of creating equity premium.

\section{Pricing kernel}

For definiteness, we shall be adopting the pricing kernel approach (see, e.g.,
Cochrane 2005, Bj\"ork 2009). We model the financial market on a probability
space $(\Omega,\mathcal{F}, \mathbb{P})$ with filtration
$\{{\mathcal F}_t\}_{t\geq0}$. Here
$\mathbb{P}$ denotes the `physical' probability measure, and
$\{{\mathcal F}_t\}$ is assumed to be generated by a multi-dimensional
Brownian motion. Expectation under
${\mathbb P}$ is denoted $\mathbb{E}[-]$, and for the conditional expectation
with respect to ${\mathcal F}_t$ we write ${\mathbb E}_t[-]$. Two other probability
measures enter the ensuring discussion; these are the risk-neutral measure
${\mathbb Q}$ and an auxiliary measure ${\mathbb R}$ to be described below.
Expectations in these measures will be written $\mathbb{E}^{\mathbb Q}[-]$ and
$\mathbb{E}^{\mathbb R}[-]$, respectively.

We assume that the market is free of arbitrage opportunities, and that there is
an established pricing kernel, but market completeness is not assumed. These
assumptions imply the existence of a unique preferred risk-neutral measure
${\mathbb Q}$. The pricing kernel, denoted here by $\{\pi_t\}_{t\geq0}$, is a
positive supermartingale with the property that if $S_T$ is the price at time $T$
of an asset that pays no dividend, then the price at time $t$ of the asset is given
by
\begin{eqnarray}
S_t = \frac{1}{\pi_t}\, {\mathbb E}_t [\pi_T S_T] .
\label{eq:1}
\end{eqnarray}
In particular, if $S_T=1$, then (\ref{eq:1}) gives the pricing formula for the discount
bond: $P_{tT} = {\mathbb E}_t [\pi_T]/\pi_t$.

We shall proceed by discussing some properties of the pricing kernel that are
relevant to our analysis here. In addition to being a positive supermartingale, the
pricing kernel fulfils the condition that ${\mathbb E}[\pi_t]\to0$ as $t\to\infty$. A
positive supermartingale possessing this property is known as a \textit{potential}.
It follows that every pricing kernel can be represented as a potential, and conversely
every potential constitutes an admissible pricing kernel. The Doob-Meyer
decomposition then shows that $\{\pi_t\}$ can be represented uniquely in the form:
\begin{eqnarray}
\pi_t = {\mathbb E}_t[A_\infty] - A_t,
\end{eqnarray}
where $\{A_t\}_{t\geq0}$ is an increasing adapted process such that $A_\infty$ is
finite. Note that ${\mathbb E}_t[A_\infty]$ is a uniformly integrable martingale. We
may define $\{A_t\}$ according to
\begin{eqnarray}
A_t = \int_0^t a_s \mbox{$\rm d$} s
\end{eqnarray}
for some adapted nonnegative process $\{a_t\}$. Hence it suffices to choose the
process $\{a_t\}$ to model the pricing kernel, and this leads to the potential
approach of Rogers (1997) to model term structure dynamics. A substitution shows
that
\begin{eqnarray}
\pi_t = \int_t^{\infty} {\mathbb E}_t [a_u] \mbox{$\rm d$} u.
\label{eq:4}
\end{eqnarray}
The representation (\ref{eq:4}) resembles that of Flesaker and Hughston (1996,1997),
if we make the following identification. First, writing $\rho_0(T) = -\partial_T P_{0T}$,
where $P_{0T}$ is the initial discount function, we see that the processes
$\{M_t(u)\}_{t\geq0,u\geq t}$ defined by
\begin{eqnarray}
M_{t}(u) = \frac{{\mathbb E}_t[a_u]}{\rho_0(u)}
\end{eqnarray}
is a one-parameter family of positive martingales, i.e. for each fixed $u\geq t$,
$\{M_t(u)\}$ is a martingale. This follows on account of the martingale property
of the conditional expectation ${\mathbb E}_t[a_u]$. In terms of these positive
martingales, the pricing kernel can be expressed in the Flesaker-Hughston
form:
\begin{eqnarray}
\pi_t = \int_t^{\infty} \rho_0(u) M_t(u) \mbox{$\rm d$} u.
\label{eq:6}
\end{eqnarray}
From the martingale representation theorem we deduce that the dynamical equations
satisfied by the positive martingale family $\{M_t(u)\}$ take the form:
\begin{eqnarray}
\mbox{$\rm d$} M_t(u) = M_t(u) v_t(u) \mbox{$\rm d$} \xi_t,
\label{eq:7}
\end{eqnarray}
where $\{v_t(u)\}$ is a family of adapted (in general vectorial) processes and
$\{\xi_t\}$ is a standard multi-dimensional
Brownian motion under the ${\mathbb P}$ measure. We observe therefore that
modelling the pricing kernel is equivalent to modelling the one-parameter family
of volatility processes $\{v_t(u)\}$. On account of (\ref{eq:6}) and (\ref{eq:7}) we
deduce, by an application of Ito's lemma, that
\begin{eqnarray}
\frac{\mbox{$\rm d$} \pi_t}{\pi_t} = -r_t \mbox{$\rm d$} t - \lambda_t  \mbox{$\rm d$} \xi_t,
\label{eq:dpi}
\end{eqnarray}
where
\begin{eqnarray}
r_t = \frac{\rho_0(t) M_t(t)}{\int_t^{\infty} \rho_0(u) M_t(u) \mbox{$\rm d$} u}
\end{eqnarray}
is the short rate, and
\begin{eqnarray}
\lambda_t = -\frac{\int_t^\infty \rho_0(u) v_t(u) M_t(u)\mbox{$\rm d$} u}
{\int_t^{\infty} \rho_0(u) M_t(u) \mbox{$\rm d$} u}
\label{eq:10}
\end{eqnarray}
is the market risk premium. The fact that the drift
of $\{\pi_t\}$ can be identified with the short rate can be seen by applying the
martingale condition (\ref{eq:1}) on the money market account $\{B_t\}$
satisfying $\mbox{$\rm d$} B_t = r_t B_t \mbox{$\rm d$} t$. That is, the drift of $\{\pi_t B_t\}$ vanishes if
and only if the drift of $\{\pi_t\}$ is $\{-r_t\}$. Similarly, let us write $\{\mu_t\}$ for
the drift of a risky asset $\{S_t\}$ that pays no dividend, and $\{-\lambda_t\}$ for
the volatility of $\{\pi_t\}$. Then the martingale condition on $\{\pi_t S_t\}$ implies
that $\mu_t=r_t+\lambda_t\sigma_t$, which shows that $\{\lambda_t\}$ indeed
expresses the excess rate of return above the risk-free rate in unit of volatility.

An advantage of working with the pricing kernel is that once a model is chosen
for the volatility processes $\{v_t(u)\}$ of the martingale family, we are able not
only to price a wide range of derivatives via the pricing formula
${\mathbb E}[\pi_T H_T]$, where $H_T$ is the payout of a derivative, but also
to obtain a model for the interest rate term structure. Furthermore, a model for
$\{v_t(u)\}$, which can be calibrated by use of market data for derivative prices,
implies a process for the risk premium $\{\lambda_t\}$ according to the
prescription (\ref{eq:10}), and this in turn can be used for asset allocation purposes.
This is the sense in
which derivative prices can be used to calibrate the risk premium, within any
modelling framework (cf. Brody \textit{et al}. 2011). The issues that we would
like to address here are: (a) the ambiguity associated with the determination of
the risk premium from market data; and (b) the identification of the origin of this
ambiguity. For these purposes, it is useful to examine the probabilistic
characterisation of the pricing kernel, within the term structure density approach
of Brody and Hughston (2001).

\section{Probabilistic representation of the pricing kernel}

To proceed, we shall make the following observation that the positivity of
nominal interest and the requirement that a bond with infinite maturity must
have vanishing value imply that $\rho_0(T) = -\partial_T P_{0T}$ defines a
probability density function on the positive half-line (Brody and Hughston 2001).
More generally, the positivity of the martingale family $\{M_t(u)\}$ implies that
$\{\rho_t(u)\}$ defined by
\begin{eqnarray}
\rho_t(u) = \frac{\rho_0(u) M_t(u)}{\int_0^{\infty} \rho_0(u) M_t(u) \mbox{$\rm d$} u}
\label{eq:12}
\end{eqnarray}
is a measure-valued process, i.e. $\rho_t(u)\geq 0$ for all $t$ and all $u$; and
\begin{eqnarray}
\int_0^\infty \rho_t(u) \mbox{$\rm d$} u = 1
\end{eqnarray}
for all $t\geq0$.
The measure-valued process thus introduced suggests the existence of a random
variable $X$ whose conditional density under some probability measure is given by
(\ref{eq:12}). Furthermore, an application of Ito's lemma on (\ref{eq:12}) shows that
\begin{eqnarray}
\frac{\mbox{$\rm d$} \rho_t(u)}{\rho_t(u)} = \left( v_t(u) - {\hat v}_t\right)
\left( \mbox{$\rm d$}\xi_t - {\hat v}_t\mbox{$\rm d$} t\right),
\label{eq:14}
\end{eqnarray}
where
\begin{eqnarray}
{\hat v}_t = \int_0^\infty v_t(u) \rho_t(u) \mbox{$\rm d$} u
\end{eqnarray}
can be thought of as the conditional expectation of $v_t(X)$.

Indeed, the dynamical equation (\ref{eq:14}) takes the form of a Kushner equation,
thus implies the existence of the following auxiliary filtering problem. For simplicity
of exposition, let us for now assume that the one-parameter family of volatility
processes $\{v_t(u)\}$ is deterministic. We introduce a probability space
$(\Omega,{\mathcal F},{\mathbb R})$, upon which $X$ is a positive random variable
with density $\rho_0(u)$. The meaning of the measure ${\mathbb R}$ will be
examined at a later point. On this probability space, consider the following
information process
\begin{eqnarray}
\xi_t = \int_0^t v_s(X) \mbox{$\rm d$} s + \beta_t ,
\label{eq:16}
\end{eqnarray}
where $\{\beta_t\}$ is an ${\mathbb R}$-Brownian motion, independent of $X$. The
task of the `observer' is thus to determine the best estimate of $X$ given the data
$\{\xi_s\}_{0\leq s\leq t}$. Assuming that the criteria for optimality is an estimator that
minimises the quadratic error, standard results in filtering theory (cf. Wonham 1965,
Liptser and Shiryaev 2001) show that the best estimate for $X$ is the expectation
of $X$ with respect to the \textit{a posteriori} density:
\begin{eqnarray}
\frac{\mbox{$\rm d$}}{\mbox{$\rm d$} u} {\mathbb R}(X<u|{\mathcal F}_t) = \frac{\rho_0(u)
\exp\left(\int_0^t v_s(u){\rm d}\xi_s - \frac{1}{2}\int_0^t v_s^2(u){\rm d}s\right)}
{\int_0^{\infty} \rho_0(u) \exp\left(\int_0^t v_s(u){\rm d}\xi_s - \frac{1}{2}\int_0^t
v_s^2(u){\rm d}s\right) \mbox{$\rm d$} u},
\label{eq:17}
\end{eqnarray}
where ${\mathcal F}_t=\sigma(\{\xi_s\}_{0\leq s\leq t})$.
Notice that the right side of (\ref{eq:17}) is in fact identical to the right side of
(\ref{eq:12}), provided that the measure change between ${\mathbb P}$ and
${\mathbb R}$ are suitably defined (recall that $\{\xi_t\}$ in the ${\mathbb P}$
measure is a Brownian motion, while in the ${\mathbb R}$ measure it is a
drifted Brownian motion of (\ref{eq:16})).

The above-specified filtering problem leads to the following probabilistic interpretation
for the pricing kernel. Writing
\begin{eqnarray}
N_t = \int_0^{\infty} \rho_0(u) \exp\left(\int_0^t v_s(u){\rm d}\xi_s - \mbox{$\textstyle \frac{1}{2}$}
\int_0^t v_s^2(u){\rm d}s\right) \mbox{$\rm d$} u
\label{eq:18}
\end{eqnarray}
for the normalisation of the conditional density $\{\rho_t(u)\}$, we see that the
pricing kernel is given by the `unnormalised' conditional probability that $X>t$:
\begin{eqnarray}
\pi_t = N_t \, {\mathbb R}_t(X>t),
\label{eq:19}
\end{eqnarray}
where for simplicity we have written ${\mathbb R}_t(-)={\mathbb R}(-|{\mathcal F}_t)$
for the conditional probability. Further, the price of a discount bond admits a
probabilistic representation in the ${\mathbb R}$ measure:
\begin{eqnarray}
P_{tT} = \frac{{\mathbb R}_t(X>T)}{{\mathbb R}_t(X>t)}.
\label{eq:20}
\end{eqnarray}
This formula shows that the price process of a discount bond is given by the
ratio of the ${\mathbb R}$-conditional probability that the positive random variable
$X$ taking values greater than $T$ and that of $X$ taking values greater than $t$.
By use of the Bayes formula, we deduce that (\ref{eq:20}) can alternatively be
expressed in the form
\begin{eqnarray}
P_{tT} = {\mathbb R}_t(X>T|X>t) ,
\label{eq:21}
\end{eqnarray}
since the set $\{X>t\}$ contains the set $\{X>T\}$. This is essentially the
representation obtained by Brody and Friedman (2009) for the discount bond
using the information-based approach to interest rate modelling.

It is worth remarking that the random variable $X$ has the dimension of time.
In Brody and Friedman (2009), $X$ was interpreted as the arrival time of liquidity
crisis, in the narrow sense of a cash demand. Hence, under this interpretation,
(\ref{eq:21}) shows that the bond price at $t$ is the probability that the timing of
the occurrence of a cash demand is beyond $T$, given that it has not yet
occurred at $t$, and given the noisy information (\ref{eq:16}) concerning the value
of $X$, in a suitably chosen measure ${\mathbb R}$.

\section{Back to the market measure}

The normalisation $\{N_t\}$ can be used to effect a measure change ${\mathbb R}
\to {\mathbb P}$. To see this, note first that the process $\{W_t\}$ defined by
\begin{eqnarray}
W_t = \xi_t - \int_0^t {\mathbb E}_s^{\mathbb R}[v_s(X)] \mbox{$\rm d$} s
\label{eq:22}
\end{eqnarray}
is an ${\mathbb R}$-Brownian motion with respect to the filtration $\{{\mathcal F}_t\}$
generated by the information process (\ref{eq:16}). In fact, this is just the innovations
representation for the filtering problem posed above. Thus, the Brownian property
can be verified by checking that $\{W_t\}$ satisfies the martingale condition:
\begin{eqnarray}
{\mathbb E}_t^{\mathbb R}\left[W_T\right] &=& {\mathbb E}_t^{\mathbb R}\left[
\int_0^T v_s(X) \mbox{$\rm d$} s + \beta_T - \int_0^T {\mathbb E}_s^{\mathbb R}[v_s(X)] \mbox{$\rm d$} s
\right] \nonumber \\ &=&
{\mathbb E}_t^{\mathbb R}\left[ \int_0^t v_s(X) \mbox{$\rm d$} s + \beta_t - \int_0^t
{\mathbb E}_s^{\mathbb R}[v_s(X)]
\mbox{$\rm d$} s \right] \nonumber \\ && +  {\mathbb E}_t^{\mathbb R}\left[ \int_t^T v_s(X) \mbox{$\rm d$} s
+ (\beta_T-\beta_t) - \int_t^T {\mathbb E}_s^{\mathbb R}[v_s(X)] \mbox{$\rm d$} s \right]
\nonumber \\ &=& W_t,
\end{eqnarray}
where we have made use of the martingale property
${\mathbb E}_t^{\mathbb R}[{\mathbb E}_s^{\mathbb R}[v_s(X)]]=
{\mathbb E}_t^{\mathbb R}[v_s(X)]$ of the conditional expectation for $s>t$,
and the tower property of
conditional expectation to deduce ${\mathbb E}_t^{\mathbb R}[\beta_T] =
{\mathbb E}_t^{\mathbb R}[\beta_t]$. Along with $(\mbox{$\rm d$} W_t)^2=\mbox{$\rm d$} t$, L\'evy's
characterisation shows that $\{W_t\}$ is an ${\mathbb R}$-Brownian motion.

On the other hand, an application of Ito's lemma on (\ref{eq:18}) gives
\begin{eqnarray}
\frac{\mbox{$\rm d$} N_t}{N_t} = {\hat v}_{t} \mbox{$\rm d$} \xi_t,
\end{eqnarray}
from which it follows that
\begin{eqnarray}
N_t = \exp \left( \int_0^t {\hat v}_{s} \mbox{$\rm d$} \xi_s - \mbox{$\textstyle \frac{1}{2}$} \int_0^t {\hat v}_{s}^2
\mbox{$\rm d$} s \right)
\label{eq:25}
\end{eqnarray}
is a positive martingale satisfying $N_0=1$. Hence $\{N_t\}$ can be used as the
likelihood process to change the probability measure. Specifically, for any
${\mathcal F}_t$-measurable random variable $Z_t$ we have
\begin{eqnarray}
{\mathbb E}_s^{\mathbb R}\left[Z_t\right] = \frac{1}{N_s}{\mathbb E}_t^{\mathbb P}
\left[N_tZ_t\right] \quad {\rm and} \quad {\mathbb E}_s^{\mathbb P}\left[Z_t\right] =
N_s {\mathbb E}_t^{\mathbb R}\left[\frac{1}{N_t}Z_t\right].
\end{eqnarray}
In particular, (\ref{eq:22}) and (\ref{eq:25}) shows that $\{\xi_t\}$ is a Brownian
motion under the ${\mathbb P}$ measure. In addition, we find that the random
variable $X$ has the same probability law under ${\mathbb P}$ as under
${\mathbb R}$, and that $X$ and $\xi_t$ are ${\mathbb P}$-independent. These
properties can be verified by showing
\begin{eqnarray}
{\mathbb E}^{\mathbb P}[\mbox{$\rm e$}^{{\rm i}(x\xi_t+yX)}]=
{\mathbb E}^{\mathbb P}[\mbox{$\rm e$}^{{\rm i}x\xi_t}]{\mathbb E}^{\mathbb P}[\mbox{$\rm e$}^{{\rm i}yX}]
\end{eqnarray}
for all real $x,y$, and calculating the right side explicitly.

We remark that the conditional probability ${\mathbb R}_t(X>t)$ appearing in
(\ref{eq:19}) can be interpreted as representing the pricing kernel in the
${\mathbb R}$ measure. Specifically, writing $\Pi_t$ for ${\mathbb R}_t(X>t)$,
we deduce from (\ref{eq:17}) that
\begin{eqnarray}
\Pi_t = \frac{\int_t^\infty \rho_0(u) \exp\left(
\int_0^t v_s(u){\rm d}\xi_s - \frac{1}{2}\int_0^t v_s^2(u){\rm d}s\right)\mbox{$\rm d$} u}
{\int_0^{\infty} \rho_0(u) \exp\left(\int_0^t v_s(u){\rm d}\xi_s - \frac{1}{2}\int_0^t
v_s^2(u){\rm d}s\right) \mbox{$\rm d$} u}.
\label{eq:27}
\end{eqnarray}
A short calculation making use of (\ref{eq:22}) shows that the
${\mathbb R}$-pricing kernel (\ref{eq:27}) can be expressed manifestly in the
Flesaker-Hughston representation:
\begin{eqnarray}
\Pi_t = \int_t^\infty \rho_0(x) G_t(x) \mbox{$\rm d$} x,
\end{eqnarray}
where $\{G_t(x)\}$ is a one-parameter family of positive $\mathbb{R}$-martingales:
\begin{eqnarray}
G_t(x) = \exp \left( \int_0^t \tilde{v}_s(x) \mbox{$\rm d$} W_t -\mbox{$\textstyle \frac{1}{2}$} \int_0^t \tilde{v}_s(x)^2
\mbox{$\rm d$} t \right),
\label{eq:29}
\end{eqnarray}
and where $\tilde{v}_t(x) = v_t(x) - {\mathbb E}_t^{\mathbb R}[v_t(X)]$. The
dynamical equation satisfied by the $\mathbb{R}$-pricing kernel therefore reads
\begin{eqnarray}
\frac{\mbox{$\rm d$} \Pi_t}{\Pi_t} = -r_t \mbox{$\rm d$} t - ({\hat v}_{t} +\lambda_t) \mbox{$\rm d$} W_t,
\end{eqnarray}
where ${\hat v}_{t} = {\mathbb E}_t^{\mathbb R}[v_t(X)]$ and
$\lambda_{t} = -{\mathbb E}_t^{\mathbb R}[v_t(X)|X>t]$.

\section{Indeterminacy of the risk premium}

Returning to the ${\mathbb P}$-measure, we recall that once a parametric model
for the martingale volatility $\{v_t(x)\}$ is chosen, then prices of derivatives will
in general depend on this model choice. Hence $\{v_t(x)\}$ can be calibrated from
derivative prices. The initial term structure density $\rho_0(u)$, on the other hand,
can be calibrated from the initial yield curve. By substituting these ingredients
in (\ref{eq:10}) we thus obtain a market implied risk premium, subject to the model
choice. Of course, any tractable model is unlikely to fit all derivative prices. One
can nevertheless ask whether it is possible to fix $\{v_t(x)\}$ in a hypothetical
situation where one has access to the totality of liquidly-traded derivative prices
and an unlimited computational resource, i.e. whether it is possible in principle to
fix $\{v_t(x)\}$ unambiguously. Perhaps not surprisingly, the answer is negative.

To see this, suppose that the volatility of the Flesaker-Hughston martingale family
is decomposed in the form
\begin{eqnarray}
v_t(u) = \phi_t(u) - \alpha_t ,
\label{eq:31}
\end{eqnarray}
where the vector process $\{\alpha_t\}$ is independent of $X$, and has no
parametric dependence on $u$. The minus sign here is purely a matter of
convention. Then writing
\begin{eqnarray}
L_t = \exp\left(-\int_0^t \alpha_s \mbox{$\rm d$} \xi_s - \mbox{$\textstyle \frac{1}{2}$} \int_0^t \alpha^2_s \mbox{$\rm d$} s\right),
\end{eqnarray}
we find that the pricing kernel takes the form
\begin{eqnarray}
\pi_t = L_t \int_t^\infty \rho_0(u)\, \mbox{$\rm e$}^{ \int_0^t \phi_s(u) {\rm d} \xi_s -
\frac{1}{2} \int_0^t \phi^2_s(u) {\rm d} s + \int_0^t \phi_s(u)\alpha_s{\rm d} s} \mbox{$\rm d$} u.
\end{eqnarray}
It follows that the price at time $t$ of a contingent claim, with payout $H_T=
h(S_T)$ at $T>t$, is given by
\begin{eqnarray}
H_t &=& {\mathbb E}_t\left[ \frac{\pi_T}{\pi_t}\, H_T \right] \nonumber \\ &=&
{\mathbb E}_t\left[ \frac{L_T}{L_t} \frac{\int_T^\infty \rho_0(u)\, \mbox{$\rm e$}^{ \int_0^T
\phi_s(u) {\rm d} \xi_s - \frac{1}{2} \int_0^T \phi^2_s(u) {\rm d} s + \int_0^T
\phi_s(u)\alpha_s{\rm d} s} \mbox{$\rm d$} u}{\int_t^\infty \rho_0(u)\, \mbox{$\rm e$}^{ \int_0^t \phi_s(u)
{\rm d} \xi_s - \frac{1}{2} \int_0^t \phi^2_s(u) {\rm d} s + \int_0^t \phi_s(u)
\alpha_s{\rm d} s} {\rm d} u} \, H_T \right] \nonumber \\ &=&
{\mathbb E}_t^\alpha\left[ \frac{\int_T^\infty \rho_0(u)\, \mbox{$\rm e$}^{ \int_0^T
\phi_s(u) {\rm d} \xi_s - \frac{1}{2} \int_0^T \phi^2_s(u) {\rm d} s + \int_0^T
\phi_s(u)\alpha_s{\rm d} s} \mbox{$\rm d$} u}{\int_t^\infty \rho_0(u)\, \mbox{$\rm e$}^{ \int_0^t \phi_s(u)
{\rm d} \xi_s - \frac{1}{2} \int_0^t \phi^2_s(u) {\rm d} s + \int_0^t \phi_s(u)
\alpha_s{\rm d} s} {\rm d} u} \, H_T \right],
\label{eq:34}
\end{eqnarray}
where we have used $\{L_t\}$ as a density martingale to change the measure.
Evidently, under the new measure ${\mathbb P}^\alpha$, the process
$\{\xi_t^\alpha\}$ defined by
\begin{eqnarray}
\xi_t^\alpha = \xi_t + \int_0^t \alpha_s \mbox{$\rm d$} s
\label{eq:35}
\end{eqnarray}
is a standard Brownian motion. Substituting (\ref{eq:35}) in (\ref{eq:34}) we deduce
that
\begin{eqnarray}
H_t =
{\mathbb E}_t^\alpha\left[ \frac{\int_T^\infty \rho_0(u)\, \mbox{$\rm e$}^{ \int_0^T
\phi_s(u) {\rm d} \xi_s^\alpha - \frac{1}{2} \int_0^T \phi^2_s(u) {\rm d} s }
\mbox{$\rm d$} u}{\int_t^\infty \rho_0(u)\, \mbox{$\rm e$}^{ \int_0^t \phi_s(u) {\rm d} \xi_s^\alpha -
\frac{1}{2} \int_0^t \phi^2_s(u) {\rm d} s} {\rm d} u} \, H_T \right],
\label{eq:36}
\end{eqnarray}
which is identical to the pricing formula under the ${\mathbb P}$ measure
had $\{\alpha_t\}$ been identically zero in
the first place, on account of the following observation. The price of the underlying
asset at time $T$ can be expressed in the form
\begin{eqnarray}
S_T = S_0 \exp\left( \int_0^T \left(r_s+\lambda_s\sigma_s-\mbox{$\textstyle \frac{1}{2}$}\sigma_s^2\right)
\mbox{$\rm d$} s + \int_0^T \sigma_s \mbox{$\rm d$} \xi_s \right),
\label{eq:37}
\end{eqnarray}
where $\{\sigma_t\}$ is the volatility of $\{S_t\}$. Now if the volatility of the
martingale family $\{M_t(u)\}$ takes the form (\ref{eq:31}), then the risk premium
can be expressed as
\begin{eqnarray}
\lambda_t = \lambda_t^\alpha + \alpha_t,
\label{eq:38}
\end{eqnarray}
where $\{\lambda_t^\alpha\}$ is the risk premium in the $\mathbb{P}^\alpha$
measure:
\begin{eqnarray}
\lambda_t^\alpha = -\frac{\int_t^\infty \rho_0(u) \phi_t(u) \mbox{$\rm e$}^{
\int_0^t \phi_s(u) {\rm d} \xi_s^\alpha - \frac{1}{2} \int_0^t \phi^2_s(u)
{\rm d}s} \mbox{$\rm d$} u}{\int_t^{\infty} \rho_0(u) \mbox{$\rm e$}^{ \int_0^t \phi_s(u)
{\rm d}\xi_s^\alpha - \frac{1}{2} \int_0^t \phi^2_s(u) {\rm d} s} \mbox{$\rm d$} u} .
\label{eq:39}
\end{eqnarray}
Substituting (\ref{eq:35}) and (\ref{eq:38}) in (\ref{eq:37}), we obtain
\begin{eqnarray}
S_T = S_0 \exp\left( \int_0^T \left(r_s+\lambda_s^\alpha\sigma_s
-\mbox{$\textstyle \frac{1}{2}$}\sigma_s^2\right) \mbox{$\rm d$} s + \int_0^T \sigma_s \mbox{$\rm d$} \xi_s^\alpha \right).
\label{eq:40}
\end{eqnarray}
We thus find that the probability law of the random variable $S_T$, and hence
$H_T$, under the ${\mathbb P}$-measure with $\alpha_t=0$, is the same as that
under the ${\mathbb P}^{\alpha}$-measure with $\alpha_t\neq0$. It follows that
any \textit{addition} of terms in the martingale volatility $\{v_t(u)\}$ that is
independent of the parameter $u$ does not affect current price levels.

The above result shows that the risk premium vector $\{\lambda_t\}$ can be
determined from market prices of derivatives only up to an additive vectorial
term $\{\alpha_t\}$. This freedom, however, is not arbitrary;  it can only
arise from a constant (i.e. independent of the parameter $u$) addition to the
volatility of the martingale family in the form of (\ref{eq:31}).

\section{Information-based interpretation}

The ambiguity in the determination of the risk premium can be interpreted from the
viewpoint of information-based asset pricing theory of Brody \textit{et al}. (2007).
In the information-based pricing framework one models the market filtration
directly in the form of an information process concerning market factors relevant
to the cash flows of a given asset. Our objective here, which extends the previous
work of Brody and Friedman (2009), is to analyse the model (\ref{eq:16}) for the
information process that determines the pricing kernel.

The interpretation of the information process (\ref{eq:16}) is as follows. Market
participants are concerned with the realised value of the random variable $X$,
which, in a certain sense can be interpreted as the timing of a serious liquidity
crisis. In reality, market participants observe price processes, or equivalently
the underlying Brownian motion family $\{\xi_t\}$. As indicated above, under the
physical ${\mathbb P}$-measure the random variables $X$ and $\xi_t$ are
independent. However, market participants `perceive' information with certain
risk adjustments characterised by the density martingale $\{N_t\}$ of (\ref{eq:25}).
In this risk-adjusted measure, the path $\{\xi_t\}$ represents the aggregate of
noisy information for the value of $X$ in the form of (\ref{eq:16}). The
`signal' concerning the value of $X$, in particular, is revealed to the market
through the structure function $\{v_t(u)\}$, which in turn determines the
volatility structure of the pricing kernel, and hence the risk premium.

Suppose that the structure function $\{v_t(u)\}$ takes the form (\ref{eq:31}),
where $\{\alpha_t\}$ is independent of $X$. Then because (\ref{eq:16})
represents the information process for the random variable $X$, the constant
$\{\alpha_t\}$ combines with the `noise' term $\{\beta_t\}$. In other words,
the choice of $\{\alpha_t\}$ is entirely equivalent to the choice of noise; the
Brownian noise is replaced by a drifted Brownian noise. This change of noise
composition does not affect current asset prices, and therefore is not
directly detectable from market data, even though asset-price drifts are
modified, in general in an unidentifiable manner. Note that the point of view
that the indeterminacy of the asset price drifts is caused by noise has been
put forward heuristically by Black (1986); our observation thus formalises this
argument more precisely.

It is worth remarking briefly the observation made in Brody and Friedman (2009)
concerning the form of the structure function $\{v_t(u)\}$ in the absence of the
noise drift $\{\alpha_t\}$. Since small values of
$X$ imply imminent liquidity crisis, in an ideal market the signal-to-noise ratio
of the information process (\ref{eq:16}) should be large for small values of $X$,
as compared to large values of $X$. In other words, under normal market
conditions we expect the signal magnitude $|v_t(u)|$ be decreasing in $u$ for
every $t$. Conversely, if $|v_t(u)|$ is increasing in $u$, then the excess rate of
return above the short rate for discount bonds, i.e. the inner product of the risk
premium and the discount bond volatility, is negative, yielding negative excess
rate of return due to the inverted form of the structure function $\{v_t(u)\}$.

\section{Anomalous price behaviour}

The fact that current asset prices are unaffected by changes in the structure of
the noise term does not imply that $\{\alpha_t\}$ can be ignored altogether. Indeed,
(\ref{eq:38}) shows that the existence of such a component does shift the
risk premium. Since the drift of an asset with volatility $\{\sigma_t\}$ is given in
the ${\mathbb P}$-measure by $r_t+\lambda_t\sigma_t$, the noise-induced
drift $\alpha_t\sigma_t$ can generate various anomalous price dynamics under
the physical ${\mathbb P}$-measure.

As an example, let us consider the case of an anomalous price growth, or a
bubble. In the large vector space of asset volatilities, it is inevitable that
volatility vectors form clusters consisting of different sectors or industries. This
is because, by definition, a given sector of companies share analogous
risk exposures. Now if an anomalous noise component $\{\alpha_t\}$ at some
point in time emerges to point in the direction of one of these volatility clusters,
then this can cause a sharp rise in the share prices of that sector. Since
the noise vector $\{\alpha_t\}$ carries no real economic information, this can
be identified as a bubble, where prices of a set of assets grow sharply, and
independently of the `true' state of affairs, without seriously affecting price
processes of other assets. Similarly, at a later time, the magnitude of
$\{\alpha_t\}$ can diminish. In particular, more reliable information concerning
the true state of affairs may be revealed, which in turn leads to an increase
in the magnitudes of volatilities on the one hand, while on the other hand the
risk premium vector can point in a direction such that the inner product
$\lambda_t\sigma_t$ takes a large negative value; thus leading to a bubble
`burst'.

In the finance and economics literature, there exists a substantial work on the
study of various aspects of financial bubbles (see, e.g., Camerer 1989 for an
early review). It is important to note that our characterisation of a bubble is
motivated by an information-based perspective. One commonly used definition
of a bubble, on the other hand, is given by the difference between the current
price and the expected discounted future cash flows in the risk-neutral
measure (cf. Tirole 1985, Heston \textit{et al}. 2007). Under this definition,
discounted asset prices in the risk-neutral measure can be modelled by use
of strict local martingales (Cox and Hobson 2005, Jarrow \textit{et al}. 2007,
2010), within the arbitrage-free pricing framework.

While this formulation of a bubble leads to the unravelling of many interesting
mathematical subtleties underlying fundamental theorems of asset pricing, from
an information-theoretic viewpoint the plausibility of such a definition for a bubble
seems questionable. In particular, a mathematical definition of a financial bubble
that involves no reference to the ${\mathbb P}$ measure seems restrictive; a
bubble, after all, is a phenomenon seen under the ${\mathbb P}$ measure.
The pricing kernel approach, on the other hand, is based on a stronger assumption
that if $\{S_t\}$ represents the price process of a liquidly traded asset, then
$\{\pi_tS_t\}$ must be a true ${\mathbb P}$-martingale. As such, the discounted
${\mathbb Q}$-expectation of future asset price necessarily agrees with the
current value, or else there are arbitrage opportunities.

The conventional definition of a financial bubble in terms of the inequality
$S_t>\pi_t^{-1}{\mathbb E}_t[\pi_T S_T]$ is sometimes justified heuristically by
the fact that some traders, when they are under the impression that there is a
bubble and thus traded prices are above the `fundamental' values, will
nevertheless participate in the apparent bubble with the view that they can
withdraw from their positions before the crunch (see, e.g., Camerer 1989 and
references cited therein). This example and other similar ones are often used in
support of the argument that some traders are willing to purchase stocks even
when they
know that the price level is above its fundamental value. The shortcomings in
such an argument are that (a) the role of market filtration is not adequately taken
into account; and that (b) the fact that such a stock purchase is equivalent to the
purchase of an American option is overlooked. A more plausible characterisation
of a bubble participation seems to be as follows. Given the information
$\{{\mathcal F}_t\}$, a trader estimates that there is a bubble that will continue
to grow for a while. Hence, subject to the filtration, the best estimate of the
future cash flow for this trader, with a suitable risk-adjustment, is given by
$\sup_{\tau}\pi_t^{-1}{\mathbb E}_t[\pi_\tau S_\tau]$, where $\tau$ is a stopping time
when the stock is sold. If this expectation agrees to the current price level, then
a transaction occurs. Conversely, it seems implausible that a transaction takes
place if the best estimate by a rational trader of a discounted cash flow is lower
than the current price level.

The view we put forward here is that a bubble in an asset ought to be identified
with an anomaly in the rate of return of that asset, and not with an anomaly in the
price level itself.
Here, a precise definition of an `anomaly' in the drift is essentially what we have
described above, namely, the existence of an additive term in the volatility of
the martingale family $\{M_t(u)\}$ that is constant in the parameter $u$. Based
on this definition, it is admissible that price processes behave in a manner that
does not always reflect what one might perceive as the true state of affairs, had
one possessed better information concerning the true worth of the assets. Put
the matter differently, decisions concerning transactions that ultimately lead to
price dynamics are made in accordance with the unfolding of information. Since
this information is necessarily noisy, the best filters chosen by market participants
will inevitably deviate from true values of assets being priced. If the noise
structure changes, then it is only reasonable that the dynamical aspects of these
deviations will likewise change. In particular, the increment of the innovations
representation---that characterises the arrival of `real' information over the
interval $[t,t+\mbox{$\rm d$} t]$---is
given by
\begin{eqnarray}
\mbox{$\rm d$} W_t = \mbox{$\rm d$} \xi_t - {\hat \phi}_t \mbox{$\rm d$} t + \alpha_t \mbox{$\rm d$} t,
\label{eq:41}
\end{eqnarray}
where ${\hat\phi}_t={\mathbb E}_t^{\mathbb R}[\phi_t(X)]$,
and this illustrates in which way the existence of a nonzero noise drift
$\{\alpha_t\}$ affects the dynamics.

Our characterisation of anomalous price dynamics is not confined to the
consideration of financial bubbles. Again, in the large vector space of asset
volatilities, it seems plausible that equity market volatilities and fixed-income
volatilities generally lie on distinct subspaces. If the noise vector $\{\alpha_t\}$
has a tendency to lie in the direction of equity-volatility subspace, then this
naturally leads to an excess growth in the equity market, explaining the
phenomena of the so-called equity premium puzzle, where over time the
rate of return associated with the equity market considerably exceeds that
of the bond market (see, e.g., Kocherlakota 1996 for a review).

\section{Relation to the risk-neutral measure}

We have established the relation between the auxiliary probability measure
${\mathbb R}$ and the physical measure ${\mathbb P}$. The relation between
the latter and the risk-neutral measure ${\mathbb Q}$, on the other, involves the
risk premium process $\{\lambda_t\}$. To recapitulate these two relations, we
have
\begin{eqnarray}
\mbox{$\rm d$} W_t = \mbox{$\rm d$} \xi_t - {\hat v}_t \mbox{$\rm d$} t \quad {\rm and} \quad \mbox{$\rm d$} W_t^* = \mbox{$\rm d$} \xi_t
+ \lambda_t \mbox{$\rm d$} t,
\label{eq:42}
\end{eqnarray}
where
\begin{eqnarray}
{\hat v}_t = \frac{\int_0^\infty \rho_0(u) v_t(u) M_t(u)\mbox{$\rm d$} u}
{\int_0^{\infty} \rho_0(u) M_t(u) \mbox{$\rm d$} u} \quad {\rm and} \quad
\lambda_t = -\frac{\int_t^\infty \rho_0(u) v_t(u) M_t(u)\mbox{$\rm d$} u}
{\int_t^{\infty} \rho_0(u) M_t(u) \mbox{$\rm d$} u} ,
\label{eq:43}
\end{eqnarray}
and where we let $\{W_t^*\}$ denote the ${\mathbb Q}$-Brownian motion. By
combining the two relations in (\ref{eq:42}) we deduce at once that the
measure-change density martingale is given by
\begin{eqnarray}
\left.\frac{\mbox{$\rm d$}{\mathbb Q}}{\mbox{$\rm d$} \mathbb{R}}\right|_{{\mathcal F}_t} = \exp\left(-
\int_0^t ({\hat v}_s+\lambda_s)\mbox{$\rm d$} W_s -\mbox{$\textstyle \frac{1}{2}$} \int_0^t ({\hat v}_s+\lambda_s)^2
\mbox{$\rm d$} s \right),
\end{eqnarray}
which determines the general relation between ${\mathbb Q}$ and ${\mathbb R}$.

As indicated above, a closer inspection on (\ref{eq:43}), however, shows that
\begin{eqnarray}
{\hat v}_t = {\mathbb E}_t^{\mathbb R}[v_t(X)] \quad {\rm and} \quad
\lambda_t = -{\mathbb E}_t^{\mathbb R}[v_t(X)|X>t] .
\label{eq:45}
\end{eqnarray}
In other words, under the restriction $X>t$, we have, conditionally, ${\hat v}_t+
\lambda_t=0$. Therefore, the auxiliary measure ${\mathbb R}$, whose existence
is ensured by the lack of arbitrage and the existence of pricing kernel, can be
interpreted as an extension of the risk-neutral measure. Conversely, by
restricting to the event $X>t$, we can think of ${\mathbb R}$ indeed as the
risk-adjusted measure.

\section{Stochastic volatility}

So far we have analysed the case for which $\{v_t(x)\}$ is a deterministic function
of time. The fact that the volatility structure of the martingale family $\{M_t(x)\}$ is
deterministic, however, does not imply deterministic volatilities for asset prices.
On the contrary, even for an elementary discount bond, the associated volatility
process is highly stochastic. Hence when we speak about a `stochastic volatility'
we have in mind the volatility for the martingale family $\{M_t(x)\}$, whereas the
stochasticity for asset prices is presumed.

From the viewpoint of practical implementation, it probably suffices to restrict
attention to deterministic volatility structures, since deterministic volatilities for
$\{M_t(x)\}$ give rise to a range of sophisticated stochastic volatility models for
asset prices. Indeed, it is shown in Brody \textit{et al}. (2011) that even in the
very restricted case of a single factor model with the time-independent volatility
$v_t(x)=\mbox{$\rm e$}^{-\sigma x}$ that depends only on one model parameter $\sigma$, it is
possible to calibrate caplet prices across different maturities reasonably accurately.

It is nevertheless of interest to enquire whether the auxiliary information process
exists in the more general context of stochastic volatilities. For this purpose, let
us begin by considering the case where $\{v_t(x)\}$ admits the decomposition
(\ref{eq:31}) and where $\{\phi_t(x)\}$ is deterministic and $\{\alpha_t\}$ is chosen
such that the noise term $n_t\equiv\int_0^t\alpha_s\mbox{$\rm d$} s+\beta_t$ is an
$\{{\mathcal F}_t^\beta\}$-measurable Gaussian process. Then an application of
the martingale representation theorem shows that $\{n_t\}$ admits a
decomposition of the form
\begin{eqnarray}
n_t = \int_0^t b_s \mbox{$\rm d$} s + \int_0^t \gamma_s \mbox{$\rm d$} \beta_s,
\end{eqnarray}
where $\{b_s\}$ and $\{\gamma_s\}$ are deterministic. A short calculation then
shows that an auxiliary information process
\begin{eqnarray}
\xi_t = \int_0^t \phi_s(X) \mbox{$\rm d$} s + n_t
\end{eqnarray}
in the ${\mathbb R}$ measure indeed exists, with the property that the scaled
information process $\int_0^t\gamma_s^{-1}\mbox{$\rm d$}\xi_s$ determines the market
Brownian motion and that $\{b_t\}$ plays the role similar to that of a
deterministic $\{\alpha_t\}$ in the previous analysis, and hence is not determinable
form current market prices.

The foregoing example shows how one can model the random rise and fall of
anomalous price dynamics. More generally, the structure function $\{v_t(x)\}$ can
depend in a general way on the history of the information process up to time $t$.
In this case, we obtain a generic stochastic volatility model for the martingale
family. Provided that the structure function is sufficiently well behaved so that
relevant stochastic integrals exist, the auxiliary information process can be seen
to exist in the ${\mathbb R}$ measure. To illustrate this, consider an elementary
`toy model' for which information process takes the form of an Ornstein-Uhlenbeck
process:
\begin{eqnarray}
\xi_t = \mbox{$\rm e$}^{\sigma X t}\int_0^t \mbox{$\rm e$}^{-\sigma Xs} \mbox{$\rm d$} \beta_s,
\end{eqnarray}
where $\sigma$ is a parameter, and $X$ and $\{\beta_t\}$ are independent. Such
an information process corresponds to a stochastic volatility model for which the
volatility process is given by a linear function of the ${\mathbb P}$-Brownian
motion: $v_t(x)=\sigma x \xi_t$.

\section{Discussion}

The main results of the paper are as follows: We have derived the existence of an
auxiliary filtering problem underlying arbitrage-free modelling of the pricing kernel;
the solution of which determines the volatility structure of the
positive martingale family $\{M_t(u)\}$ appearing in the Flesaker-Hughston
representation for the pricing kernel. We have demonstrated that the structure of
the ambient information process fully characterises the risk premium process
$\{\lambda_t\}$. We have shown, under the Brownian-filtration setup, that
$\{\lambda_t\}$ admits a canonical decomposition into two terms in an additive
manner; the systematic term that can be calibrated from current market data for
derivative prices, and the idiosyncratic term that cannot be estimated (unless, of
course, one can estimate drift processes of risky assets), and thus can be
identified as noise.

It is worth emphasising that these results hold irrespective of our choice of
interpretation. Nevertheless, our characterisation of anomalous price dynamics
seems sufficiently compelling, for, such phenomena are ultimately observed
under the physical measure ${\mathbb P}$. One might ask what causes the
evolution of the noise drift $\{\alpha_t\}$. This is an interesting
econometric question that, however, goes beyond the scope of the present
investigation. It
suffices to remark that the random variable $X$ that constitutes the signal
component of the ambient information process has units of time, and thus is
ultimately linked to the term structure of financial markets. One possible
explanation of the excess equity premium therefore is that fixed-income market
intrinsically embodies more information concerning the term structure as
compared to the equity market, and this imbalance is manifested in the form of
an additional drift in the noise component pointing generally towards the
direction of equity volatility vectors.

\vskip 10pt

\noindent The authors thank Mark Davis, Robyn Friedman, Matheus Grasselli,
Lane Hughston, Andrea Macrina, and Bernhard Meister for comments and
stimulating discussions.

redpajama_set_name: RedPajamaArXiv


text:
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Steel Prices Rise -- Again
Increasing demand, a weaker dollar and higher input costs mean consumers will pay more.
By Tonya Vinas
Just when they thought they would get a break on steel prices again, U.S. manufacturers are facing rising prices prompted by a healthier domestic steel industry and a host of global forces.
As of press time, a ton of hot-rolled sheet steel was approaching $400, up more than $50 per ton from early winter and about $100 from January 2002.
Pittsburgh-based United States Steel Corp. announced it will raise prices $50 to $60 per ton in April, and many steel makers such as Cleveland-based International Steel Group are adding surcharges to cover increases in their costs. Industries that rely heavily on steel, such as automobiles, consumer durables and construction, are facing a potentially drastic rise in costs this year.
For instance, when Caterpillar Inc., Peoria, Ill., announced fourth-quarter earnings in January and projected a 12% rise in sales, the company said it expects to pay more for steel. Director of investor relations Nancy Snowden said the company would offset the spike with cost cutting, as it has in the past.
U.S. steel producers say the rise in prices reflects higher raw-materials and transportation costs and a recovery in their industry, which started a rapid decline in 2001 following a surge of cheaper imports and an implosion of pension and retiree health-care costs. According to the American Iron and Steel Institute (AISI), a lobbying group for North America's largest producers, steel prices in the United States remain below other countries' and are actually moving closer to normal. Two years ago, when hot-rolled sheet was selling for less than $250 a ton, producers were selling so far below costs that many mills filed for bankruptcy and shut down. (Quoting data from "Purchasing" magazine, AISI says the average price for hot-rolled steel during the period 1980-2000 period was $339 per ton and peaked at $400 in 2003 following imposition of the president's order for steel tariffs on imports.)
Indeed, while the steel tariffs drove up prices for U.S.-made steel in 2002 and 2003, it appears now that prices are being affected more by global forces -- including greater demand and lower inventories. According to MEPS, a UK steel consultancy and research company, $400 per ton is the global average for hot-rolled sheet, and world consumption of steel is expected to reach 1 billion tons this year, more than 100 million more tons than was consumed in 2001. About 80% of this year's increase will come from Asia, particularly China.
Additionally, a weaker U.S. dollar means imported steel -- a cheaper alternative in recent years -- is now selling at a much higher price.
Steel prices soar in the UAE
Steel price increases in the UAE are worrying for contractors, reported Construction Week. Eight months ago steel was Dhs800 a tonne, now it is close to Dhs2,000. This is a problem for fixed price contracts, but for new tenders prices will be inflated to accomodate higher steel costs.
China's Need for Metal Keeps U.S. Scrap Dealers Scrounging
The New York Times | March 13, 2004 | ANDREW POLLACK and KEITH BRADSHER
LOS ANGELES, March 12 — At a time when toys, televisions and other products made in China are flooding into the United States, helping push the trade deficit to record levels, there is at least one American product for which China has a nearly insatiable demand — industrial junk.
Sales of scrap metal to China have surged, with effects that are ricocheting across the American economy. Prices are soaring not just for scrap, but for metals in general. After years of surpluses that forced many steel makers into bankruptcy, supplies are so tight that contractors told a Congressional hearing in Washington this week that they sometimes cannot obtain supplies at any price.
China last year became the first country ever to import more than $1 billion of American scrap, according to the newspaper American Metal Market. Indeed, it would not be an exaggeration to say that China's transformation into an industrial powerhouse is being fueled by America's waste, and that of other countries, as well. Much of the material being used to build China's skyscrapers, factories and telecommunications systems — along with many of the products it exports — is derived from scrap, which is usually cheaper than new metal made from ore.
"China is very hungry," said David Pan, a Chinese-born scrap metal buyer, as a truck carrying steel reinforcing bars from a dismantled building in San Diego prepared to dump its cargo with a deafening clatter on the floor of his warehouse in Maywood, an industrial town just south of here. "They need a lot of material."
A decade ago, Mr. Pan was working in a Los Angeles restaurant when relatives back in China asked him to start buying scrap. Now, as China booms, so does Mr. Pan's business, called Universal Scrap Metals. He ships about 500 containers a month to China filled with battered pipes, fine metal shavings, doorknobs, jumbles of wire, crumpled cars and all other manner of flotsam. He is even negotiating to buy the remains of a steel factory in Utah; he would ship it, as scrap, to his native country.
American scrap dealers, an industry of 1,200 or so mainly mom-and-pop operations, are sharing in the boom times.
"They're scrounging every yard in the country, like a vacuum cleaner," Ely Keenberg, president of Ekco Metals, a Los Angeles scrap dealer, said of purchasers from China. At one point during an interview, Mr. Keenberg's receptionist interrupted to show him the business card of a man from Hong Kong who had just made a cold call looking for scrap. "If we allowed it, we'd have one in here every five minutes," said Mr. Keenberg, who sells 90 percent of his scrap to Chinese buyers.
American companies that depend on scrap are, in the meantime, scrounging.
"We're having greater and greater difficulty in securing scrap," said M. Brian O'Shaughnessy, chief executive and principal owner of Revere Copper Products in Rome, N.Y., a company founded by Paul Revere that turns copper scrap into sheets and strips. "It's causing the price of scrap to go through the ceiling."
Both copper and steel industry trade groups are drawing up petitions that would ask the government to temporarily limit scrap exports — an authority that Washington has used only once, in the mid-1970s.
The price of scrap steel has soared to more than $300 a ton, compared with about $156 a ton at the end of 2003 and $77 at the beginning of 2001, according to the Emergency Steel Scrap Coalition, a group backed by steel users and minimills, which use scrap to make about half of the nation's steel. Many minimills have imposed surcharges to pass the higher costs onto customers like automobile and construction companies, with some of them resisting.
"Scrap is the overwhelming factor determining steel prices at this point," said Christopher Plummer, managing director of Metal Strategies, a consulting firm in West Chester, Pa.
Rising exports are clearly one factor behind the high prices, but the extent to which they can be blamed is debated. Over all, exports of steel scrap have almost doubled since 2000 to 11.9 million tons last year, close to a record. China was the largest importer, accounting for 3.5 million tons, or about 30 percent, of the exports.
But scrap dealers argue that exports are still small compared with domestic consumption of about 70 million tons a year, and so could not account for the huge price increases. Moreover, they note, there have been several occasions in the last two decades when total scrap exports reached or even exceeded last year's levels.
"What is happening now is not unique," said Robin Wiener, president of the Institute of Scrap Recycling Industries, the dealers' trade group. Attempts to restrict scrap exports, she said, are "just clearly a smoke screen attempt to control the price of scrap" and would be a "distortion of free trade."
Some experts add that in any event, China's building boom has the look of a bubble and cannot last indefinitely. Indeed, China's State Development and Reform Commission just announced that after fixed investment in steel mills rose 90 percent last year, it would stop approving virtually all applications to build mills. Still, with many mills approaching completion, one Chinese trade group forecasts that imports of scrap will nearly double by 2005 over last year's levels.
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Home Russia & China China China drowns out critics of lifetime Xi Presidency
China drowns out critics of lifetime Xi Presidency
Amer Zafar Durrani
AFP |
China's propaganda machine kicked into overdrive on Tuesday to defend the Communist Party's move to lift term limits for President Xi Jinping as criticism persisted on social media in defiance of censorship.
The party has shocked many observers by proposing a constitutional amendment to end the two-term limit for president, giving Xi a clear path to rule the world's second largest economy for life.
Censors have scrambled to block critical comments on social media but users of the Twitter-like Weibo website continued to speak out on Tuesday, two days after the party's announcement.
China cannot stop and take a break. Our country must not be disturbed by the outside world or lose our confidence as the West grows increasingly vigilant toward China.
"So pathetic, we have 1.3 billion people, no one can resist," wrote one user.
Another lamented the lack of political reform: "I once believed that I could see a president elected by one man, one vote in my lifetime."
Censors blocked searches for the phrases "I object", "proclaimed king", "tenure system" and "Winnie the Pooh" — the portly cartoon bear to which Xi has been compared.
Xi is expected to secure a second five-year term when the rubber-stamp National People's Congress opens its annual plenary session on Monday.
State-run media published new editorials praising the Central Committee's proposed amendment, which is expected to be approved during the legislative session and would allow Xi to stay in power beyond 2023.
Read more: Iran sticking to nuclear deal: UN watchdog
The China Daily, an English-language newspaper, said the party's decision "has been necessitated by the need to perfect the Party and the State leadership system".
The daily said the party has always proposed amendments that "have injected new ideas and concepts about where the country will go and how it will achieve its goal of rejuvenation and ensure people live happier lives".
The Global Times, a nationalist tabloid, was even more profuse in its praise of the amendment in an editorial titled "Constitution change responds to new era".
Since Xi took power as party chief in 2012, it wrote, "the new ruling team has not just been muddling along under the leadership of General Secretary Xi Jinping. Instead, it quickly started to deepen reforms in a comprehensive and magnificent way".
Read more: Xi poised to extend power as China set to lift term.
The newspaper took a shot at the political system of the United States and Europe.
"It has shaped and affected quite a few Chinese people's mind-sets. But some key parts of the Western value system are collapsing. Democracy, which has been explored and practiced by Western societies for hundreds of years, is ulcerating," it said.
UNSC to discuss Kashmir issue, will the UN fulfill its purpose?
Trump, the deal maker, blinks before China
Taiwan added to the list of US weapons against China
Lockheed Martin in India: Strategic implications for Pakistan
Female cops under investigation for posting steamy Instagram selfies
Making a success story out of CPEC: Certain, probable, or doubtful?
First cargo train from China leaves for Karachi


If I had to pick my favourite way to earn a living, photographing dogs playing with toys would be near the top of the list. So when Bionic asked me if I was interested in photographing their toys, I jumped at the chance and frankly went a little overboard. But I couldn't seem to stop myself. I was having way too much fun.
First up was Skorch – the cutest little jack russell. His mom wasn't too sure how well he would fetch but we decided to give it a try anyway. She shouldn't have worried. He was awesome. And he really loved the little bone. He laid there and chewed on it with no encouragement from us.
Next, I met with Journey and her dad. I knew Journey from daycare and was sure she'd be perfect for the job. She is toy crazy and gorgeous – what more could I ask for? We met down at Popson in the evening and were able to get a few water pictures (the toys float) as well as some silhouettes too. I LOVE the way the bone glowed orange in the silhouettes.
These are just a few of my favourites from my first day of shooting. I'll share more with you tomorrow! Lots more to come.


One of the best things about being a mum in 2017 is the ability to be completely candid and share our experiences of motherhood. This is also one of the worst things. Never before has mum life been so under the microscope or so laid bare for all to see.
Instagram, YouTube, blogs and Facebook mean many of us – bloggers or not – put little elements of our life out there all the time for everyone to see. Sharing all these details of our lives lays us all open to criticism. Whether you're a cupcake baking mum or a fish finger serving mum, you can't please everyone and there's a high chance someone somewhere will silently (or not so silently) judge you. They'll either assume you don't love your kids because you moan about them, or think you need to get a life and stop being so sentimental because you love your kids too much. As I said, you can't please everyone. This is just life as a parent in 2017.
There was an article published in the Daily Mail today which slated a few mum bloggers, one of whom is a good mate of mine. This post isn't about that article specifically (which was pretty vile even for Daily Mail standards), but it's a catalyst to something I was going to write anyway about the idea of "keeping it real" as a mum.
This phrase of "keeping it real" is bandied around all the time online. I hate it. I use it often myself, because I'm too lax to think of a better term, but I still hate it. I know, I'm a bad, bad person.
Anyway, the reason I hate the term "keeping it real" is because it suggests the alternative is a pack of lies. For example, I might vlog about a family day out and include the toddler throwing food in the air and getting naked. This doesn't mean another vlogger's family picnic without a naked food-throwing toddler is any less real though. Maybe their kids simply don't like getting naked and throwing food around. Lucky them.
I've always been an original Inbetweener. I wasn't in any particular gang at school, college or uni and don't easily fall into a clique of mums in the school playground (although our school is so small you could argue we're all just one big clique anyway!). And just like at school, in blogging I count bloggers on both sides of the invisible "realness" fence my buddies.
Anyway, the phrase "keeping it real" suggests, to me, that if you don't blog or vlog about the bad bits of life then you're basically a fake. This simply isn't the case. Of course we all choose what we put out there when we share bits of our life online, but even the edited bits are real. There's only so much you can fake, after all.
Take my videos over on YouTube, for example. They couldn't be any more different to my pal Katie's. That doesn't mean I dislike Katie or think her videos are fake. Of COURSE they're not. Katie's videos – just like mine – show HER experiences as a mum.
Obviously this isn't to say there aren't some people out there faking it. Whether it's mums pretending to have had a bad day for likes on Facebook or mums pretending to be the next Stepford Wife for views on YouTube, obviously there are some people out there who do this. I mean, come on, there are so many of us online these days it's an inevitability isn't it? But I'd like to think these mums are in the minority – and, anyway, faking it is pointless because you can sniff it from a mile off. Most of us are just sharing our days in all their perfect or imperfect glory.
So, in short, if you're a mum and you pop up in my Facebook feed venting about a difficult bedtime with the kids, or sharing some photos of a brilliant family day out, I won't judge you. I know you're "keeping it real", because all our versions of reality are different on any given day.
My other thought regarding what I choose to share about my child is not really about how I want to come across as a person but is always whether I will be comfortable showing my children what I shared of their lives – whilst in person I might describe an action as being taken by "that little sh*t" I personally probably wouldn't share that where it could come back to haunt me at a later date… sharing in person with context, gestures and so forth is one thing, but things seem much more deliberate and callous when they are written down I think – I personally think the best humorous writers manage to elude things without spelling them out!
Really interesting comment, thank you Rachel! I agree, it's a fascinating debate. For me, I think there's huge value in being really candid about the difficult sides of parenting as it helps other parents who might be having a tough time. I agree it's important to think about the future ramifications of what we write. I'm always aware of this but I think, ultimately, if our kids know they are loved and adored (which they do) then they'll understand that sometimes we had tough days. I think the Mail article failed to realise how much value there is in sharing these hard parts of being a parent and how many mums have been personally really helped by blogs like The Unmumsy Mum and Hurrah for Gin. The whole thing of writing about lives online is a huge and fascinating subject though isn't it?


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Children as young as 14 are becoming addicted to e-cigarettes, head of Britain's biggest addiction clinic says
Since 2015, it has been illegal for retailers to sell e-cigarettes to anyone under 18
Camilla Turner, Education Editor
1 March 2019 • 9:00pm
Camilla Turner
Children as young as 14 are becoming addicted to e-Cigarettes, the head of Britain's biggest addiction clinic has said.
John Dicey, chief executive of Allen Carr's Easyway which has 35 centres around the UK, said there has been a steep rise in the past year of young people seeking help on how to quit vaping.
"We have noticed a sharp increase in the last half of 2018 and first quarter of 2019 in the number of inquiries from youngsters - and their parents - who took up vaping in their early teens and now wish to quit," he said.
Numbers are "in the dozens rather than in hundreds" he said, but added that there has been a "clear sea change in the past few months", which reflects the surge of youth enquiries from America since 2017.
Mr Dicey, who is a senior Alan Carr therapist, explained how a "significant" number of teenagers that come for treatment said they were encouraged to vape instead of smoke by their parents, particularly if their parents are smokers.
How an E-cigarette works - desktop
Since 2015, it has been illegal for retailers to sell e-cigarettes to anyone under 18 but a subsequent operation by Trading Standards found that 40 per cent of shops allowed teenagers aged 14-17 to purchase the devices, which are also sold online.
"Children can start on e-cigarettes at quite a young age, around 12 to 14-years-old, when they get passed around the class," Mr Dicey said.
"There are all sorts of flavours - candy floss, popcorn – it's all seen as a bit of fun. We are getting some youngsters coming in who have started vaping, having not smoked before."
In response to the growing numbers of enquiries about e-cigarette addiction among youngsters, Allen Carr's Easyway is now designing a new treatment course specifically aimed at teenagers who want to quit vaping, and another for their parents.
Last year, Allen Carr centres in the UK treated 630 adult vapers and "dual users", meaning people who vape as well as smoke. This represents around 9 per cent of all clients and an increase of over 50 per cent on 2017. A quarter of those vapers were exclusively addicted to vaping.


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Classic Car Appraisal Services in Votaw, Texas
If you are like us, you love your car. You have probably spent countless hours and dollars making it everything you have always dreamed of. We, like you, enjoy being around car people, and more importantly cars themselves.
Although car people love to spend time and money on their cars, they all too often forget to properly value their car for insurance purposes. Dollar after dollar goes in, but never gets properly documented so that if a catastrophic event strikes, the real cost of putting the car back together gets paid by the insurance company. As collector car owners ourselves, we understand the importance of our product first hand. Fill out the form on the right to get started on your on-site Votaw car appraisal.
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Votaw United States
Facts about Votaw
Votaw is an unincorporated community in northwestern Hardin County, Texas, United States. It is part of the Beaumont–Port Arthur Metropolitan Statistical Area.
The community was named for Clark M. Votaw, assistant land commissioner of the Kirby Lumber Company and vice president of the Santa Fe Townsite Company, which laid out the town lots.
The West Hardin County Consolidated Independent School District serves area students.
When the Gulf, Colorado and Santa Fe Railway began construction on a line from Cleveland to Silsbee, the heavily wooded area of northern Hardin County was opened up for intensive lumbering. The little community that grew up around one new sawmill was named for Clark M. Votaw, assistant land commissioner of the Kirby Lumber Company and vice president of the Santa Fe Townsite Company, which laid out the town lots. A post office was established there in 1901; the town lots appear in tax records the following year. Votaw's population has remained between 100 and 200 since 1925. The timber around the community supported the area's early residents; as late as 1947 a logging camp and planing mill operated nearby, and the town shipped pulpwood, logs, staves, poles, and railroad ties. Votaw has since become a center for local agriculture. Nearby deposits of oil, discovered in 1958, continued to produce in 1984, further supplementing the local economy. In 1990 the population was 160. The population remained unchanged in 2000.
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This year's podcast section blew up like never before, and it's a testament to the power of the DJ, we suppose, who brings all the fanfare and flourishes of a hot night out to the banal locale of our desktop. Out of the 50+ mixes that premiered on our website over the year, the 10 below are not only the best executed, most unique, and wholly memorable (even controversial at times), but also the sets we personally keep returning to when in need of a solid DJ mix. Enjoy.


"Girl Story," 2014. Winner, Juror's Merit Award, "All-Alaska Juried XXXV," Anchorage Museum at Rasmusson Center.
"Girl Story 2," 2014. Exhibited in QUILTS=ART=QUILTS, Nov. 1, 2014 - Jan. 4, 2015, Schweinfurth Art Center, Auburn NY.
"Girl Story" is a textile series I imagine I will work on for years. It feels like drawing from a well that will never run dry. The pieces employ ink, heavy, frantic hand embroidery and vintage textiles and were initially intended to explore menarche and the idea that every woman, every girl, has a story around this passage into womanhood. And what started out as a personal journey, a way to get my thoughts straight on how I could be an empowering figure in my own young daughter's life, has ended up touching other lives; women are coming forward with stories of other losses and renewal. Some of these losses I have never experienced nor can I fathom. These aren't vague blog post comments I'm receiving. These are purposeful letters. Women are stopping me and looking me in the eye. They have a story to tell. I promised I would listen, so I am.
I've been given permission to share letters here between a woman and her mother (now in her 70's and requesting anonymity). They were written in direct response to the blog post "A history of pretty," which explores the impetus for embarking on this series. The photographs in this post are from my own experience, cataloguing the time the and thought and essence of this project thus far.
I received these letters in reverence.
I hope you will read them with the same.
...the article kind of left me with the feeling of "how can anything so every day-ish" be talked about in such length. Using washable pads was nothing unusual when I first got my period. Sometimes you could see them even on clothes lines drying after the family wash day. But when small children asked what that thing was, it was talked about in hushed voices. I remember seeing buckets of them, filled with cold water for soaking before washing them. When the first disposables came out, it was heaven. No more dealings with the bloody bucket, which by the way also had to be hidden, if possible.
When I listened to the video, I felt different. Remembering how I felt during my first period at age 13, it did feel almost like a celebration to me. Maybe it should be? I felt, like now I was a woman!! (Hahah) Most of my friends already had their periods and now I finally entered that "sisterhood". You could talk to them about your cramps, how heavy or regular or irregular you were, etc. I always disliked references like "got my monthly visit" and others that made it sound like it was something to be embarrassed about and you couldn't speak of it. It is more important as many smaller things we celebrate, like "Grandparents Day" or "Valentine's". Without it, where would humanity be? I liked her linking it to the waxing and waning of the moon. I read somewhere a long time ago, that periods of all the females in a family correlate to a great extent with the full moon, I don't know if that is true, but I do remember when all of you were home, it seemed like I had to buy one pack of sanitary napkins after another until we were all through and then we had a period of time when nobody needed them.
I would like to hear your thoughts on it.
"Girl Story 2" in the show Quilts=Art=Quilts at the Schweinfurth Art Center, Auburn, NY.
... I found Amy's quilting to be visually a bit disturbing because it was so familiar and so private, hung out there as it is for public viewing -- a little like the clothesline you wrote about. Even so, it has a beauty that reflects on the notion of menses itself. I felt the essay that accompanied the quilt was outstanding and gave me much to think about.
My response to Amy's art is layered and goes deep into what it meant to raise sons rather than daughters, for which I was always grateful. It has taken me 53 years, and growing beyond childbearing years, to feel truly comfortable in my own body. If menstruation had only been a stain of blood each month, it would have been easy to deal with. Instead, the hormonal fluctuations each month often created a sense of insecurity and distrust in my own assessment any given situation. I was okay on my own and my mood seemed manageable when it was just me and the kids. But when my now ex-husband was home, it was a time of heightened anxiety, fraught with emotional landmines. I could deal with the physical pain, cramps, fatigue, headaches. I just wasn't good at dealing with the difficulties, long-inherent in our relationship, during "that time of the month." Without those hormonal fluctuations, I might have trusted my intuitions more, realizing that maybe I wasn't "crazy" after all.
I always felt lucky to be raising sons because I didn't feel equipped to raise daughters. Life seemed far too complicated for women and I was having enough of a time navigating my female life much less helping a child feel confident enough with her femininity to grow into secure womanhood. Boys by contrast seemed like uncomplicated creatures. Snakes and snails and puppy dog tails. Now of course I see things very differently. If I'd had a daughter, my intuition would have grown more keen on behalf of a girl whose well being I would have fiercely protected. I say this because I now have a granddaughter and I enjoy great clarity -- there is nothing muddled about nurturing her whole person. I also see that boys are equally as sensitive to gender issues and equally as confounded by the roles of men and women in the arenas of power and vulnerability. Male or female, the human psyche is especially tender in the area of sexuality, especially as it plays out in the crucible of early family life.
All that is to say, Amy's work made me dig deep into my own memories and thoughts about being a woman over the years. I do remember the first time I needed napkins and how you, Mom, made me feel special about joining the sisterhood of women. I remember thinking I was now grown up enough to have a baby. That was mind blowing for a 14 year old. (I was a late bloomer.) You always made us feel like being a woman was a fine thing and that it would and should not impede anything we ever wanted to achieve. You offered unconditional support and love even during the times our journeys were difficult for you to watch. All of your daughters have been richly blessed.


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Professor Victor Mayer Amédée Mannheim
(b.) -
(d.)
After graduating from the École d'Application in Metz, Mannheim he became an officer of the French artillery. It was while he was a student at the École d'Application that the ideas for the slide rule came to him. He invented what may be considered the first of the modern slide rules around 1850. This was a new scale system that used a runner to perform calculations. The Mannheim rule, which also brought into general use a cursor, or indicator, was much used in France, and after about 1880 it was imported in large numbers into other countries. Although slide rules existed before his time, invented by Oughtred and Gunter and others, it was he who standardized the modern version of the slide rule which was in common use until pocket calculators took over a few years ago. After several years in the military, he was appointed to the École Polytechnique in Paris, while continuing his army career. In 1864 he was appointed as Professor of Descriptive Geometry at the École Polytechnique. He retired from his army post in 1890, having attained the rank of colonel in the engineering corps. He continued teaching at the École Polytechnique until he retired in 1901 at the age of 70. He made numerous contributions to geometry and for his outstanding contributions to the subject he was awarded the Poncelet Prize of the Académie des Sciences in 1872. He studied the polar reciprocal transformation introduced by Chasles and applied his results to kinetic geometry. His own definition of kinetic geometry considered it to be the study of motion of a figure without reference to any forces, time or other properties external to the figure. He also studied surfaces, in particular Fresnel's wave surfaces.
Inventor of a type of slide rule which was in common use until pocket calculators took over a few years ago
Historical Pioneer (Pre-Moderns)


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Reviews - Mystery
Fire & Ice (A Mauzzy and Me Mystery, #2)
Polcari
YOUNG ADULT: Sara Donovan is working as an intern at the Carlton Museum when her great observation skills, intuition, and a good measure of pertinacity throw her into the middle of a well-orchestrated crime within the museum. Her pet and faithful companion, Mauzzy, is the only one who has knowledge of the mishap.
Brooke Hamilton, a private investigator, has just taken on a huge case that could prove to be too dangerous for her. Even her criminal law father suggests the case is too large for her, especially if her prime suspect is powerful and wealthy. Detective Gabriel O'Reilly gets put on the case with her to investigate the races being rigged and the possible jockey homicide.
Concession Stand Crimes (The Ballpark Mysteries Book 2)
Asselin
Madeline Boucher has had a lot to deal with. Now she is helping to run her family's baseball team. Murder comes to the park when a brewery heiress is murdered and the body is found in the stands. Madeline finds herself thrust into an investigation with a long list of suspects.
Herbs and Homicide (Heywood Herbalist Cozy Mysteries Book 1)
In an attempt to throw away her Hollywood stardom which left her hurt and alone, Samantha RathBone, now going by the name Sam Jones, finds refuge in the small town of Heywood. Bonnie, the owner of Sage Advice, takes Sam under her wings and offers her a job and a place to stay.
Platform Shoes: A Steve Daniels Mystery Book 1
It's 1943 and Steve Daniels has had a lot to deal with in the last few years. Injured while serving his country in France, now he's back in the States to teach in San Antonio, Texas. What's difficult for him are the nightmares and memories of what he went through overseas. What he didn't expect was to meet a woman who would turn his world upside down.


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In support of the success of our client communities, our services go well beyond construction to aid in the marketing of the community. From sales models and mock ups to video updates and live job site web cameras, we take potential new residents along through the construction journey. Benchmark Construction will even work with you to create a virtual design which paired with visualization software helps your new residents choose the final finishes for their new home.
Our senior living construction portfolio includes some of the most popular and marketable communities in Central Pennsylvania.
Creating innovative solutions that serve the unique needs of senior living communities is our passion.


Located in the Villuercas-Ibores-Jara region, the Extremadura Geological Park was created on 17 September 2011. There are eight such parks in Spain, of which this is the only one in this area. The park covers nineteen towns and is a symbol of sustainable tourism based on geo-conservation. A geological site declared by UNESCO's General Conference.
And if this isn't enough to attract you to this unique landscape, you might just be tempted by the views from its highest point, Risco de La Villuerca at 1,601 metres, the dividing point for Extremadura's two great river basins, the Tagus and the Guadiana. This gives you a panoramic view over the mountain chains and valleys, and the other 44 outstanding geosites in the Geopark.
Start your visit at the Cañamero visitors' centre, where you can find out all about the area's history.
One of the area's major attractions is its paleontological riches, dating back some 540 million years to when this region was part of a primordial sea. This is demonstrated by huge folds and fault lines, and eroded and sedimentary forms.
You can discover numerous traces of human history, in the form of boulders with ancient paintings and dolmens, hill forts, castles and unique Mudejar architecture, which you can fully experience at the Guadalupe Monastery World Heritage site.
Mining was also present in the area, and you can experience this by visiting the Costanaza mine at Logrosán. There are also eight routes around the area: one takes you to one of the main geosites in the area, the Castañar de Ibor cave. It is no longer possible to visit the cave itself, but you can find out all about it in the visitors' centre.
And there's more... If you love good food, come and try some of the area's traditional delights, such as goat's cheese, honey, wines, cherries, chestnuts and traditional pastries. Delights that will make you want to return again and again.


Sony won't feat a internal 10-bit 422 recording anytime soon.
Sony is very protective about their higher end products, they haven't even offered 10-bit 422 externally, much less internally, something that is only available from the FS7 and above, not even the FS5 has internal 10-bit 422 recording.
There is a reason Sony still hasn't fixed overheating, why the A6300 doesn't even have IBIS or why despite people actually wanting one, there is no A7000.
Don't count on Sony to get the same feats as the GH5, even internal 4K took quite some time before Sony was able to catch up anyway.
4K 10-bit 4:2:2 is amazing! However, I need Dual-Pixel Auto Focus in my cameras from now on. If this has movie autofocus that works as well as the 1DX Mk II or 5D Mk IV then I'm definitely buying it. Otherwise, I'll probably stick with Canon for the time being.
I know this is the Internet, but for those that watched the presentation, this is still a product in development and one that isn't final nor they had released the full final specs, so unless Panasonic says so, omission is far from the same as a sure thing that it won't have some feat.
People need to be patience and wait for the full announcement, just be happy that the internal 10-bit 422 recording is true despite the odds, this camera is still a few months away from shipment.
That said, it would be wise for Panasonic to at least address the IBIS, so people can either freak out or calm down.
Imo the only company that could have done something similar (actually even better imo) in late 2016/early 2017 could have been Samsung with nx1-mk2. Since we won't ever see this camera, I guess sony will come with something competitive, but not sooner than 2018.
The NX1 was released less than two years ago. Realistically a mind blowing camera isn't going to come out every six months.
The "see in the dark" camera requests are ridiculous, but on the budget end of the spectrum silky smooth 3200 ISO is a bit hard to find. Even that video didn't for example have a model standing under a street light at 1 am. The stuff in the store windows was lit by indoor spotlights and everything on the street was really dark.
I use a BMPCC and have had hotpixel issues when lifting shadows at ISO 1600. Bulletproof 3200 ISO coupled with a speedbooster would be a god send.
Yeah, I think you are probably right.
If Panasonic can deliver as they did with the GH4 then that will push others, who in turn will push the GH6 until we end up with a Godlike all-seeing prosumer unit for £200 come 2025.
GH5 looks like a winner. Amazing features.
I hope the 10bit is at a high bitrate. Low bitrate 10bit is rubbish.
Shame it can't do 4K 60FPS in 10bit. Hopefully the high-frame-rate 1080P is in 10bit.
I wonder if they'll opt for H265 in the end? Time will tell.
Yeah A7S iso's are crazy and are almost never needed. However a clean iso 1600 or 3200 would be very welcome. Like when you are running run and gun with an anamorphic lens, and you can only open up to 2.8 or 5.6 and you do not have access to any lights (yeah I know it is like 0,00001% of you guys that are doing this, but this is something that I would welcome). I dont need IBIS or autofocus. I shoot with manual lenses and I use grip to stabilize (gymbals, dolly's, glidecams).
- hopefully the image is better then the GH4 with a external recorder.
I'm not panicking, the camera is 6 months or more from being released, but its a feature that would have certainly been highlighted at the presentation or the presser. If its in there, it would have been a part of the presentation. None of the Panny's have PADF, no surprise that the GH5 doesn't either.
It still looks like a great mockup/specsheet. Like I said, looking for to samples, whenever they actually surface.
This camera will be dead serious about video! Nice! But first I'm just going to get the Pana G8x and Oly E-M1 mark II I think to replace the G7, GX80 and E-M1. Pretty much covers every basic need. For more control and possibilities however, the GH4 might just have to make way for that GH5 with LOG, anamorphic ratios/de-squeeze, pro audio solution, battery life etc. Although, I wouldn've have minded if they had something between the GH and the VariCam line-up for video. Something in the direction of the Kinefinity Terra. Basically all the GH5 mojo but not inside a GH4-style body, but a Terra-like body. But who knows what the future holds!
A few weeks ago it was 'no way Panasonic' will do internal 10-bit', now it's 'Sony will trump it before it's released'.
No way. Sony don't even have 10-bit 4K in the FS5. They have higher end ranges to protect.
So what are we looking at here? $2k for the body?
I was about to sell my MFT gear. Now I'm thinking if waiting might be better. This camera looks indeed amazing!
But as a previous guy, I really hope the AF is good. The reason why I'm with canon DSLRs as my main tool, even though the video is meh, is dual pixel AF. It's just THAT good. Not even the a6300 can reach it at the moment. Don't care about IBIS, but please superb autofocus!
With what Olympus just announced, I think that Panasonic is working on something to improve AF as well. I'll worry about AF later when they fully announce the GH5 but before that Panasonic does need to address IBIS to the public.
I hope we get surprised with a big autofocus improvement on the GH5. In the meantime, I have my eye on that EM1-mkII.
I don't know if it has been mentioned, but the latest I hear is that it is a 18mp sensor. Not 20.
I think that the 6K photo burst extraction feature is actually a tip off to the GH5 doing 6K full uncropped (<2x of FF) 16:9 sensor width readout and down-sampling to 4k, which hopefully matches the a6300's high-res detail.
There's no reason to write off the possibility of external 10-bit 4:2:2 4k60p.
I'm still nervous it might not have IBIS or good on-sensor PDAF.
Has anyone heard anything about whether the automatic anamorphic crop mode of the GH4 has been retained/improved? Or will it require manual post-processing?
I am guessing if the Olympus EM 1 ii can have 121 cross-point on-chip PDAF, then obviously there seems no reason why the Panasonic GH5 should have far better focus for Photo, and a much higher burst rate.
I am guessing the PDAF is a fabrication process, on existing sensors, and is not very difficult. Though for mirrorless cameras, since everything is electronic, it may be an issue of processing power. And that is why Panasonic may also need a pair of quad core processors, one solely for focus. This may be a blessing for both photo and video. If Canon and Sony can do it, I see no reason why Panasonic cannot do it too.
Also, there is some kind of Focus Improvement in the FZ2000 which is noticeable from its fake dolly zoom feature. It doesn't lose focus while zooming in. I am guessing Panasonic is Already working on PDAF in a huge way.
I read in some Fuji interview that faster focussing needs much lighter moving parts within the lens. And that is why their new lenses are being planned accordingly.
We basically just got a Hint of the GH5's features. It is going to be a real powerhouse.
I wonder what the 4k crop will be if it's 20mp? ~2.5x? yikes. Possibly downsampled?
Though for mirrorless cameras, since everything is electronic, it may be an issue of processing power. And that is why Panasonic may also need a pair of quad core processors, one solely for focus.
Panasonic will probably have to throw in fast processors because it must handle 4K 60p and 10bit 422, so I think they will have horse power covered.