text:
\section{INTRODUCTION}
Jump processes have become increasingly popular in financial modeling since the seminal work of \cite{Merton1976} (see, e.g., \cite{Kou2002} and \cite{KouWang2004}). \cite{ContTankov} provides a comprehensive exposition of the use of jump processes in financial modeling. The CGMY model of \cite{CGMY2002} is one of the most popular jump processes.

CGMY processes are flexible price models that exhibit infinite activity and can be of either finite variation (i.e., with stability index $0<Y<1$) or infinite variation (i.e., with stability index $1\leq Y<2$). Since its inception, the CGMY model has found  success  in modeling both asset returns and option pricing. \cite{CGMY2002} calibrated the CGMY model to both time series and options data. Their empirical results show that equity prices are pure jump processes of infinite activity. Although statistical processes for equity prices are estimated to be of infinite variation in a few particular circumstances, they are typically of finite variation. Risk-neutral processes for equity prices are all estimated to be of finite variation. The modeling flexibility of the CGMY model can be understood as follows. \cite{MadanYor} showed that a CGMY process can be represented as a Brownian motion time-changed by an independent subordinator that is usually referred to as the time change of the CGMY process. In fact, in the early 1970s, in the context of the modeling of asset prices, \cite{Clark1973} had already introduced the idea of time change, which can effectively capture such stylized empirical facts as fat-tailedness and skewness for the distribution of observed asset returns. \cite{AneGeman} later extended this idea to the modeling of the flow of market information by time changes in explaining the normality of observed asset returns. In option valuation, \cite{CGMY2003} found clear advantages of CGMY models endowed with stochastic volatility over other L\'evy models endowed with stochastic volatility in terms of reproducing the volatility skew pattern.

Nonetheless, one challenging problem with these otherwise appealing jump models is to find a sequential sampling (or path simulation) method that is pertinent to pricing path-dependent options.

In the finite-variation case (where the stability index $0<Y<1$), exact simulation methods are available. In this case, the density of the CGMY increment is an exponentially tilted density of a unilateral stable random variable, and therefore the standard rejection sampling method can be applied. However,  simple rejection sampling suffers from low acceptance rates in certain regions of  parameter space. To overcome this shortcoming of the simple rejection method, \cite{Devroye} developed an exact double rejection method with uniformly bounded complexity over all parameter ranges.

In the infinite-variation case (where the stability index $1\leq Y<2$), all available sampling methods entail approximations.  Utilizing the time change representation, \cite{MadanYor} developed a sequential simulation method for the CGMY model through sequentially sampling the increments of its time change. This method consists of two steps. In the first, one truncates and approximates the contribution of small jumps in the series representation for a $Y/2$-stable subordinator, following the approach of \cite{AsmussenRosinski}. Second, based on the approximated $Y/2$-stable process, one further applies the rejection method of \cite{Rosinski} to obtain (approximate) samples from the time  change process of the CGMY model. \cite{BallottaKyriakou} have developed a sampling method based on inverse Fourier transformation and the computing technique of fast Fourier transformation (FFT). This method involves three layers of approximation errors, namely, the regularization error from approximating the distribution of the CGMY (or the CGMY time change) increment by a regularization technique (cf. \cite{Hughett}), the truncation error from truncating the infinite integration domain of the inverse Fourier transformation integral, and the discretization error from applying the FFT technique. In simulation pricing of derivatives, it is difficult to quantify and bound the biases of Monte Carlo price estimates caused by the aforementioned approximation errors over the whole parameter space. \cite{PoirotTankov} developed an exact simulation pricing method, which does not introduce biases in price estimates, by exploiting the fact that under an appropriate change of measure, a CGMY process is a stable process whose increments can be sampled exactly; however, their method does not provide direct access to the sample paths of a CGMY process.

In pricing such path-dependent options as lookback and barrier options, \cite{KimKim2016} have recently developed a bridge sampling scheme (although only for the finite-variation case) that can lead to savings of simulation costs when combined with adaptive sampling techniques and to variance reduction when combined with stratified sampling techniques. This bridge sampling method is based upon saddle-point approximations for the related probability density functions and is otherwise comparable in cost and accuracy to the existing rejection sampling method when generating a fixed number of observations. However,  extension of this bridging sampling scheme to the infinite-variation case is nontrivial and has yet to be done.

In this paper, we develop a new and easy-to-implement sequential sampling method for  CGMY models   with either finite or infinite variation. As we shall see, our method involves only one simple error term, which has a transparent interpretation. To be specific, based on the time change representation of a CGMY process presented in \cite{MadanYor}, we find that the time change subordinator can be further decomposed into two independent components, namely, a finite generalized gamma convolution\footnotemark\footnotetext{The generalized gamma convolution law was introduced by \cite{Thorin} and studied by \cite{Bondesson}. See also, e.g., pp. 351--354 in \cite{JRY} for a comprehensive review on this class of distributions and processes.}  subordinator and an error term. For the first component, the increment of a finite generalized gamma convolution subordinator can be represented in distribution  as the product of a gamma random variable and another independent Dirichlet mean random variable (see, e.g., \cite{JamesBernoulli,JamesLamperti}). While the gamma random variable can be generated by standard procedures, the Dirichlet mean random variable can be sampled exactly via the double CFTP scheme of \cite{DevroyeJames}. As far as the error term is concerned, we show that it can be bounded and made arbitrarily small in  the $L^1$ sense.

In simulating Dirichlet mean random variables, the (exact) double CFTP method may have an excessive computational budget for certain parameter ranges. To reduce simulation costs with virtually no  loss of accuracy, an approximation scheme can be adopted instead of the double CFTP scheme. This approximate sampling method utilizes a special series representation of the Dirichlet mean random variable that converges exponentially fast, allowing approximation errors to be easily kept arbitrarily small.

We close this section by emphasizing the following aspects of our contribution:
\begin{itemize}
\item We have discovered a \emph{path} simulation method for the CGMY processes   with either finite or infinite variation, with approximation errors that have a \emph{transparent} interpretation, namely, that the approximation error bounds ($\varepsilon$ and $\tilde{\varepsilon}$ in Sections \ref{subsec:error} and \ref{subsubsec:APPscheme}) control the $L^2$ distance between the approximate variate and the target CGMY increment (see Remark \ref{rem:discLONEerror} and the discussion immediately following (\ref{eq:GHWstoppingN})).
\item As discussed above,  existing methods, which must entail approximations in the infinite-variation case, do not share this unique  feature of our method, and hence  it is difficult for them to quantify the biases of  Monte Carlo price estimates when simulating prices of financial derivatives.
\end{itemize}

The rest of this paper is organized as follows. In Section \ref{CGMYintro}, we provide a brief introduction to the CGMY model and related derivative pricing problems. Section \ref{subsec:exactmethodYzeroone} provides an exact path simulation method for the finite-variation case, which is less familiar in the context of CGMY processes than in the context of tempered stable processes. The main results on the decomposition of the CGMY time change and the associated path simulation schemes are given in Section \ref{subsec:between02}. Section \ref{sec:numerical} is devoted to numerical studies where we compare our proposed method with existing methods for simulating prices of both path-independent and path-dependent options. We conclude in Section \ref{sec:conclusion}. The proof of Theorem \ref{prop1} and the sampling algorithms are presented in the appendices.

\section{THE CGMY OPTION VALUATION MODEL}\label{CGMYintro}
A CGMY process $X=\{X(t),t\geq0\}$ is a pure jump L\'evy process with $X(0)=0$ and L\'evy density
\begin{align}\label{eq:LevyDensityCGMY}
\nu_X(x)=C\left(\frac{e^{-G|x|}}{|x|^{1+Y}}I\left\{x<0\right\}+\frac{e^{-Mx}}{x^{1+Y}}I\left\{x>0\right\}\right),
\end{align}
where $C>0,$ $G\geq0,$ $M\geq0,$ and $0<Y<2$ are four parameters. $Y$ is usually referred to as the \emph{stability index}. When $0<Y<1$ (respectively, $1\leq Y<2$), the CGMY process is of finite (respectively infinite) variation.

The characteristic function ($Y\neq1$) of $X(t)$ is given by
\begin{align}\label{eq:CharacteristicFunctionCGMY}
{\rm E}\left[e^{iuX(t)}\right]=\exp\left\{tC\Gamma(-Y)\left[(G+iu)^Y-G^Y+(M-iu)^Y-M^Y\right]\right\}.
\end{align}
The risk-neutral asset price process $S=\{S(t),t\geq0\}$ under the CGMY model is defined as
\begin{align}\label{eq:RiskNeutralAssetPrice}
S(t):=S(0)\exp\{(\omega+r-q)t+X(t)\},
\end{align}
where $r$ is the (constant) risk-free interest rate, $q$ is the asset's continuously compounded dividend yield, and $\omega$ is chosen such that the discounted asset price is a martingale, or, in other words,
$$
{\rm E}\left[\exp(\omega t+X(t))\right]=1.
$$
This condition and (\ref{eq:CharacteristicFunctionCGMY}) imply that
\begin{align}
\omega=-C\Gamma(-Y)\left[(G+1)^Y-G^Y+(M-1)^Y-M^Y\right],\notag
\end{align}
where $M\geq1$ is required to ensure that ${\rm E}[S(t)]<\infty$ for all $t\geq0$.

The present fair value $c$ of a derivatives contract with general payoff $f(\{S(t),0\leq t\leq T\})$ at maturity $T$ is given by
$$
c={\rm E}[e^{-rT}f(\{S(t),0\leq t\leq T\})].
$$
Different forms of payoff function $f(\cdot)$ correspond to different derivatives contracts. If one can perfectly generate, say, $I$ independent and identically distributed (i.i.d.) sample paths $(S^{(i)})_{1\leq i\leq I}$ from $S$, then the Monte Carlo estimate of the derivative price $c$ is given as follows:
\begin{align}\label{eq:mcmcprice}
\hat{c}=\frac{1}{I}\sum_{i=1}^Ie^{-rT}f(\{S^{(i)}(t),0\leq t\leq T\}).
\end{align}

Let $0\equiv t_0<t_1<t_2<\ldots<t_n\equiv T$ be discrete monitoring times, $K$ the strike price, and $\mathcal{B}$  a prescribed barrier level; then the following provide four examples of payoff functions for four different derivatives contracts:
\begin{itemize}
\item European plain vanilla call option: $f(\{S(t),0\leq t\leq T\})=(S(T)-K)^+$;
\item floating strike lookback call option: $f(\{S(t),0\leq t\leq T\})=(S(T)-\max_{0\leq i\leq n}S(t_i))^+$;
\item up-and-in call barrier option: $f(\{S(t),0\leq t\leq T\})=(S(T)-K)^+1_{\{\max_{0\leq i\leq n}S(t_i)>\mathcal{B}\}}$;
\item Asian call option with discrete monitoring: $f(\{S(t),0\leq t\leq T\})=\left(\frac{1}{n+1}\sum_{i=0}^nS(t_i)-K\right)^+$.
\end{itemize}
In all cases, Monte Carlo simulation pricing reduces to simulation of increments of the log return process $X$ in (\ref{eq:RiskNeutralAssetPrice}). In the following two sections, we introduce new sequential sampling schemes for simulating increments of the CGMY log return process.

\section{AN EXACT METHOD FOR $Y\in(0,1)$}\label{subsec:exactmethodYzeroone}
It is notable that exact simulation schemes are less familiar in the context of CGMY processes than in the context of tempered stable processes. In this section, we elaborate on how exact sampling methods for tempered stable processes can be adapted to sampling CGMY increments in the finite-variation case.

From (\ref{eq:LevyDensityCGMY}), $X$ has the following difference-of-CGMY  representation:
\begin{align
X(t)=X^+(t)-X^-(t),\notag
\end{align}
where $X^+=\{X^+(t),t\geq0\}$ and $X^-=\{X^-(t),t\geq0\}$ are two independent L\'evy processes with L\'evy densities
\begin{align}\label{eq:differenceCGMYlevyDens}
\nu_{X^+}(x)=C\frac{e^{-Mx}}{x^{1+Y}}I\left\{x>0\right\} ~~~{\rm and~~~}\nu_{X^-}(x)=C\frac{e^{-Gx}}{x^{1+Y}}I\left\{x>0\right\},
\end{align}
respectively.

When $0<Y<1$, the exact sampling method of \cite{Devroye} for exponentially tilted stable distributions can be adapted to the simulation for the CGMY increments. Observe that the CGMY process with $0<Y<1$ can be represented as a difference of two independent increasing L\'evy processes with L\'evy densities (\ref{eq:differenceCGMYlevyDens}). Hence, it suffices to consider the simulation problem for these increasing positive processes, i.e., subordinators. We take the simulation of process $X^+$ with L\'evy density $\nu_{X^+}(x)$ for illustration. Then the simulation of process $X^-$ with L\'evy density $\nu_{X^-}(x)$ follows similarly. As a consequence, the CGMY process $X$ is given by the difference between $X^+$ and $X^-$.

Without loss of generality, we only need  consider the simulation of variables $X^+(t)$ for $t>0$, because L\'evy processes have the stationary increments property. The distribution of $X^+(t)$ is exponentially tilted stable, i.e.,
$$
X^+(t)\overset{d}=\lambda^{1/Y}\mathcal{S}_{Y,M\lambda^{1/Y}},
$$
where $\lambda:=tC\Gamma(1-Y)/Y$, and $\mathcal{S}_{Y,M\lambda^{1/Y}}$ is an exponentially tilted stable random variable that has density function $$e^{M^Y\lambda-M\lambda^{1/Y}x}g_{Y}(x),~~~ x>0,$$
where $g_{Y}(x)$ is the density of the unilateral $Y$-stable random variable with Laplace transform
$$\int_0^\infty e^{-\mu x}g_Y(x)\,dx=e^{-\mu^Y},~~~ \mu>0.$$

\cite{Devroye} proposed a double rejection method for the exact simulation of an exponentially tilted stable random variable that can be uniformly fast over all parameter ranges. Based on \cite{Devroye},  a double rejection algorithm for generating random variable $X^+(t)$ is given in Section \ref{subsec:appdoublerejection}.

\section{THE MAIN RESULTS FOR $Y\in(0,2)$}\label{subsec:between02}
We now turn to the general case where the CGMY processes can be of infinite variation.
\subsection{A Decomposition of the CGMY Time Change}
\cite{MadanYor} showed that a CGMY process can be represented as a time-changed Brownian motion as follows:
\begin{align}\label{eq:TimeChangedCGMY}
X(t)=\theta \mathcal{T}(t)+W(\mathcal{T}(t)),
\end{align}
where $\theta=(G-M)/2$, and $W=\{W(t),t\geq0\}$ is a standard Brownian motion that is independent of the time change subordinator $\mathcal{T}=\{\mathcal{T}(t),t\geq0\}.$ \cite{MadanYor} identified the L\'evy density of $\mathcal{T}$ as follows:
\begin{align}\label{eq:LevyDensTimeChangeCGMY}
\nu_{\mathcal{T}}(x)=C\frac{2^{Y/2-1}\Gamma(Y/2)}{\Gamma(Y)}\frac{e^{-(\tilde{\theta}^2-\theta^2)x/2}}{x^{1+Y/2}}{\rm E}\left[\exp\left(-\frac{\tilde{\theta}^2x}{2}\frac{\gamma_{Y/2}}{\gamma_{1/2}}\right)\right],
\end{align}
where $\tilde{\theta}=(G+M)/2$, and $\gamma_{Y/2}$ and $\gamma_{1/2}$ are independent gamma random variables with unit scales and shapes $Y/2$ and $1/2$, respectively.\\

The following theorem provides a decomposition of the time change $\mathcal{T}$, facilitating the path simulation of both finite- and infinite-variation CGMY processes:
\begin{theorem}\label{prop1}
For $L>0$ and fixed $t>0$, the time change subordinator $\mathcal{T}(t)$ in (\ref{eq:TimeChangedCGMY}) has the following decomposition:
\begin{align}
\mathcal{T}(t)=\mathcal{T}_L(t)+\epsilon_L(t),\label{eq:timechangedecomposition}
\end{align}
where $\mathcal{T}_L(t)$ and $\epsilon_L(t)$ are independent and have the following distributional properties:
\begin{itemize}
\item[(i)] $\mathcal{T}_L(t)$ is a generalized gamma convolution random variable that has Laplace exponent

    $$-\log\left({\rm E}\left[e^{-\mu\mathcal{T}_L(t)}\right]\right)=\frac{2\widetilde{C}L^{Y/2}}{Y}{\rm E}\left[\log\left(1+\mu R\right)\right],$$
    where $\mu>0$, $\widetilde{C}:=tC2^{Y/2-1}/\Gamma(Y)$, and the random variable $R$ is given by
    $$
    R:=\frac{1}{\frac{GM+\tilde{\theta}^2\mathcal{R}}{2}+\mathcal{Z}},
    $$
    where $\mathcal{R}:=\gamma_{Y/2}/\gamma_{1/2}$ is independent of $\mathcal{Z}$, which has probability density function $f_{\mathcal{Z}}(z)=YL^{-Y/2}/2z^{Y/2-1},$ $0\leq z\leq L$;
\item[(ii)] The standardized $\epsilon_L(t)$ has a standard normal limiting distribution as $L\to\infty$. In particular,
\begin{align}{\rm E}[\epsilon_L(t)^2]\leq\frac{\widetilde{C}^2}{(1-Y/2)^2L^{2-Y}}+\frac{\widetilde{C}}{(2-Y/2)L^{2-Y/2}}.\label{eq:errorbound}\end{align}
\end{itemize}
\end{theorem}

From (\ref{eq:errorbound}), we can see that $\epsilon_L(t)=O_p(1/L^{1-Y/2})$. Hence, we can choose some large $L$ such that $\epsilon_L(t)$ is negligible. Then we can use samples of $\mathcal{T}_L(t)$ to approximate that of $\mathcal{T}(t)$ given that we can simulate $\mathcal{T}_L(t)$ perfectly. In Section \ref{subsec:perfectsimGGC}, we show that exact simulation of $\mathcal{T}_L(t)$ is possible.

\subsection{Perfect Simulation of $\mathcal{T}_L(t)$}\label{subsec:perfectsimGGC}
We explain how $\mathcal{T}_L(t)$ can be exactly sampled. Let $$\tau:=\frac{2\widetilde{C}L^{Y/2}}{Y}.$$
We have shown in Theorem \ref{prop1} that $\mathcal{T}_L(t)$ is a generalized gamma convolution random variable with Laplace exponent
\begin{align}
\tau{\rm E}\left[\log\left(1+\mu R\right)\right].\label{eq:laplaceexpGGC}
\end{align}
From \cite{JamesBernoulli}, a generalized gamma convolution random variable $\mathcal{T}_L(t)$ with Laplace exponent (\ref{eq:laplaceexpGGC}) has the following representation (see also \cite{JRY}):
\begin{align}\label{eq:gammamitureofrepGGC}
\mathcal{T}_L(t)\overset{d}=\gamma_{\tau}\cdot \mathcal{D}_{\tau}(F_R),
\end{align}
where $\gamma_{\tau}$ is independent of $\mathcal{D}_{\tau}(F_R)$, $\gamma_{\tau}$ is a gamma random variable with shape $\tau$ and unit scale, and $\mathcal{D}_{\tau}(F_R)$ ($F_R$ denotes the cumulative distribution function of random variable $R$) is a Dirichlet mean random variable that solves for random variable $\mathcal{D}$ in the following stochastic equation (see \cite{JamesLamperti}):
\begin{align}\label{eq:dmeanstochasticequation}
\mathcal{D}\overset{d}=\beta_{1,\tau}R+(1-\beta_{1,\tau})\mathcal{D},
\end{align}
where $\beta_{1,\tau}$ is a beta random variable with parameter values ($1,\tau$), and the random variables on the right-hand side of  (\ref{eq:dmeanstochasticequation}) are independent of one another.

By (\ref{eq:gammamitureofrepGGC}), simulation of $\mathcal{T}_L(t)$ reduces to  simulation of a gamma random variable $\gamma_{\tau}$, which is available in most standard numerical libraries, and  simulation of a Dirichlet mean random variable $\mathcal{D}_{\tau}(F_R)$, which we elaborate upon below.

\cite{DevroyeJames} devised an exact sampler termed  double CFTP (``coupling from the past'') for generating random numbers from the steady-state Markov chain distribution (of $\mathcal{D}$) determined by the following generic stochastic equation:
\begin{align}\label{eq:srochasticequationgeneral}
\mathcal{D}\overset{d}=BQ+(1-B)\mathcal{D},
\end{align}
where  double CFTP requires that the density function $h(\cdot)$ of the random variable $B$ can be precisely evaluated and is bounded from below on $[0,1]$ by a constant $c_h>0$, $0<Q\leq c_Q<\infty$, with $c_Q$ being a constant, and again the random variables on the right-hand side of the above equation are independent of one another. The double CFTP algorithm for generating random numbers from $\mathcal{D}$ in (\ref{eq:srochasticequationgeneral}) is given in Section \ref{subsec:doublecftp}.

When $B=\beta_{1,\tau}$ and $Q=R$ in (\ref{eq:srochasticequationgeneral}), we recover (\ref{eq:dmeanstochasticequation}), and the solution to $\mathcal{D}$ is just the Dirichlet mean random variable $\mathcal{D}_{\tau}(F_R)$.  Because the density function of $\beta_{1,\tau}$ takes the form $h(x)=\tau(1-x)^{\tau-1}$ for $x\in[0,1]$ and $R\leq2/(GM)$, in the Dirichlet mean case, the requirements of the double CFTP scheme, namely, that the density function $h(\cdot)$ of the random variable $B$ can be precisely evaluated and is bounded from below on $[0,1]$ by a constant $c_h>0$ and that $0<Q\leq c_Q<\infty$, are satisfied with $c_Q=2/(GM)$ and $c_h=\tau$ when $0<\tau\leq1$.

It appears that in practice, $0<\tau\leq1$ is a tight constraint for the double CFTP scheme to be applicable. Nonetheless, when $\tau>1$, we can always decompose $\mathcal{D}_{\tau}(F_R)$ as
$$
\mathcal{D}_{\tau}(F_R)\overset{d}=\sum_{j=1}^J\frac{\gamma_j\mathcal{D}_{\tau_j}(F_R)}{\gamma},
$$
where $J$ is an integer, $\tau=\sum_{j=1}^J\tau_j$ for $\tau_j>0$, $\gamma=\sum_{j=1}^J\gamma_j,$ $\gamma_j$ are independent gamma random variables with shapes $\tau_j$ and common unit scale, $\mathcal{D}_{\tau_j}(F_R)$ are independent Dirichlet mean random variables with shapes $\tau_j$ and common scale variable $R$, and $\gamma_j$ are independent of $\mathcal{D}_{\tau_j}(F_R)$. \cite{JKZ:2013} provide the optimal choices of $J$ and $\tau_j$ as $J=\lfloor \tau\rfloor+1$ and $\tau_j\equiv\tau/J$. Therefore, the requirement $0<\tau\leq1$ of  double CFTP poses no difficulty for the simulation of Dirichlet mean random variables with bounded scale random variable $R$.

\begin{remark}\label{rem:ontauLY}
Concern might be expressed about the effects of the range of $\tau$ on the computational complexity of simulations using the double CFTP sampler, since larger $\tau$ means that more random numbers need to be generated. Recall that $\tau=2\widetilde{C}L^{Y/2}/Y=(2L^{Y/2})tC2^{Y/2-1}/(\Gamma(Y)Y).$ For fixed $t$, $C$, and $L$, the denominator of $\tau$ , i.e., $\Gamma(Y)Y$, is bounded from below by a strictly positive constant for $Y\in[0,2]$, indicating that $\tau$ does not blow up with $Y$. Therefore, the computational complexity of a simulation depends mainly on $L$. To be precise, when $t$ and the  parameters $C$ and $Y$ are held constant, $\tau$ increases with $L$. $L$ is usually large, since this is necessary to ensure that the error term $\epsilon_L(t)$ in (\ref{eq:timechangedecomposition}) is negligible. It is easy to see that, with the remaining parameters held constant, $\tau$ increases faster with $L$ when $Y$ is larger.
\end{remark}

\subsection{The Error Term $\epsilon_L(t)$}\label{subsec:error}
In this subsection, we study the error term $\epsilon_L(t)$  in the decomposition (\ref{eq:timechangedecomposition}) of Theorem \ref{prop1}. For convenience, we recall here the inequality (\ref{eq:errorbound}):
$$
{\rm E}[\epsilon_L(t)^2]\leq\frac{\widetilde{C}^2}{(1-Y/2)^2L^{2-Y}}+\frac{\widetilde{C}}{(2-Y/2)L^{2-Y/2}},
$$
where $\widetilde{C}:=tC2^{Y/2-1}/\Gamma(Y)$. This inequality provides an upper bound on the second moment of $\epsilon_L(t)$. Holding the model parameters and $t$ constant, for any small $\varepsilon>0$, one can choose $L$ such that both two terms on the right-hand side of (\ref{eq:errorbound}) are less than or equal to $\varepsilon^2/2$. The smallest $L$ that satisfies this requirement is given by
\begin{align}\label{eq:Lchoice}
L_{\rm min}=\max\left\{\left(\frac{2\widetilde{C}^2}{\varepsilon^2(1-Y/2)^2}\right)^{1/(2-Y)},\left(\frac{2\widetilde{C}}{\varepsilon^2(2-Y/2)}\right)^{1/(2-Y/2)}\right\}.
\end{align}
If $L$ is chosen as in (\ref{eq:Lchoice}), then, by Jensen's inequality, we have
$$
{\rm E}|\epsilon_L(t)|\leq\varepsilon.
$$
Hence, for $\epsilon_L(t)$ to be negligible, one only need  prescribe a precision $\varepsilon$ and then choose $L=L_{\rm min}$ as above. Of course, smaller $\varepsilon$ leads to larger $L_{\rm min}$ and hence greater computational effort in simulating $\mathcal{T}_L(t)$ using the double CFTP scheme. Moreover, when $\varepsilon$, $t$, and other model parameters are fixed, $L_{\rm min}$ increases with $Y$, and hence, in order to achieve the  same precision, the double CFTP method is more time-consuming for larger $Y$ than for smaller $Y$. This situation can be challenging when $Y$ approaches 2.

\begin{remark}\label{rem:discLONEerror}
Recall that the CGMY increment has the time change representation (\ref{eq:TimeChangedCGMY}), i.e., $X(t)=\theta \mathcal{T}(t)+W(\mathcal{T}(t))$, and, from Theorem \ref{prop1}, we have that the time change has the decomposition $\mathcal{T}(t)=\mathcal{T}_L(t)+\epsilon_L(t)$. We can thus write the CGMY increment as follows:
 $$X(t)\overset{d}=\underbrace{\theta\mathcal{T}_L(t)+\sqrt{\mathcal{T}_L(t)}W_1(1)}_{X_1(t)}+\underbrace{\theta\epsilon_L(t)+\sqrt{\epsilon_L(t)}W_2(1)}_{X_2(t)},$$
where $W_1(1)$ and $W_2(1)$ are two independent standard normal random variables that are independent of the remaining random variables on the right-hand side of the above equation. Because we can perfectly sample from the distribution of $\mathcal{T}_L(t)$ as in Section \ref{subsec:perfectsimGGC} and hence from the distribution of $X_1(t)$ that is used to approximate $X(t)$, it is easy to see from the representation of $X_2(t)$  that the $L^1$ bound $\varepsilon$ of $\epsilon_L(t)$ actually controls the $L^2$ distance between the approximate variate $X_1(t)$ and the target CGMY increment $X(t)$. Therefore, in this sense, we can say that the errors involved in our method have a transparent interpretation (see also the discussion immediately following (\ref{eq:GHWstoppingN})).
\end{remark}

\subsection{An Approximation Scheme for Simulating $\mathcal{T}_L(t)$}\label{subsubsec:APPscheme}
From Remark \ref{rem:ontauLY} in Section \ref{subsec:perfectsimGGC} and the discussions in Section \ref{subsec:error}, we notice that the suggested double CFTP scheme in Section \ref{subsec:perfectsimGGC} may be time-consuming for certain parameter ranges, for example, when $Y$ approaches 2 while  other parameters are held fixed. Therefore, we need to find an alternative method that can allow significant savings in simulation costs with virtually no loss of accuracy compared with the  exact simulation of $\mathcal{T}_L(t)$ provided by the double CFTP sampler. In this subsection, we shall introduce an approximation method that serves this purpose.

To understand the approximation scheme, we need to note that the Dirichlet mean random variable $\mathcal{D}_{\tau}(F_R)$ in (\ref{eq:gammamitureofrepGGC}) has the following series representation:
\begin{align}\label{eq:DmeanseriesRep}
\mathcal{D}_{\tau}(F_R)\overset{d}=\sum_{i=1}^\infty \tilde{B}_iR_i,
\end{align}
where
$$
\tilde{B}_1=B_1~~~{\rm and}~~~\tilde{B}_i=B_i\prod_{j=1}^{i-1}(1-B_j),~i\geq2,
$$
$B_i,~i=1,2,\ldots,$ are i.i.d. random variables equal in distribution to the beta random variable $\beta_{1,\tau}$ in (\ref{eq:dmeanstochasticequation}), and, independently, $R_i,~i=1,2,\ldots,$ are i.i.d. random variables that have the same distribution as the random variable $R$ defined in Theorem \ref{prop1}. The series representation (\ref{eq:DmeanseriesRep}) can be seen as a result of the definition of Dirichlet mean random variables in \cite{CifarelliRegazzini} and the stick-breaking random probability measures studied in \cite{IshwaranJames}, to which we refer for a complete history of those concepts.

Now we are ready to present the approximation scheme. Because the random variable $R$ is bounded by $2/(GM)$, we can adopt the method of \cite{GHW} in simulating $\mathcal{D}_{\tau}(F_R)$. Let
\begin{align}\label{eq:GHWstoppingN}
\mathcal{N}:=\min_n\left\{n:2/(GM)\left(1-\sum_{i=1}^n\tilde{B}_i\right)<\tilde{\varepsilon},~n=1,2,\ldots\right\},
\end{align}
which is a stopping time indicating when we should stop the simulation of $\mathcal{D}_{\tau}(F_R)$ according to the infinite series (\ref{eq:DmeanseriesRep}). The approximate variate $\mathcal{D}^{\mathcal{N}}_{\tau}(F_R)$ for $\mathcal{D}_{\tau}(F_R)$ is thus  given by
$$
\mathcal{D}^{\mathcal{N}}_{\tau}(F_R):=\sum_{i=1}^\mathcal{N} \tilde{B}_iR_i.
$$
The random number generation in sampling $\mathcal{D}^{\mathcal{N}}_{\tau}(F_R)$ is otherwise quite straightforward. The stopping rule (\ref{eq:GHWstoppingN}) leads to the following distance bound, which is an {\it exact} bound (rather than in the $L^1$ sense):
$$
|\mathcal{D}^{\mathcal{N}}_{\tau}(F_R)-\mathcal{D}_{\tau}(F_R)|\leq\tilde{\varepsilon}.
$$
Therefore, a sufficiently small threshold $\tilde{\varepsilon}$ can make subsequent Monte Carlo estimates virtually bias-free.

The computational complexity of this method depends on $\mathcal{N}$ in (\ref{eq:GHWstoppingN}), which determines the number of random variables that we need to simulate. The left-hand side of the inequality in (\ref{eq:GHWstoppingN}),
$$
2/(GM)\left(1-\sum_{i=1}^n\tilde{B}_i\right),
$$
gives an upper bound on the tail of the series (\ref{eq:DmeanseriesRep}). By simple calculation, we find the expectation of this quantity to be
$$
{\rm E}\left(2/(GM)\left(1-\sum_{i=1}^n\tilde{B}_i\right)\right)=\frac{2}{GM}\left(\frac{\tau}{1+\tau}\right)^n,
$$
meaning that on average the tail of the series (\ref{eq:DmeanseriesRep}) decreases exponentially fast to zero (i.e., the series converges exponentially fast), provided that $2/(GM)$ and $\tau$ take moderately sized values.

\begin{remark}
When we consider the simulation of increments over small time intervals, which is especially pertinent to pricing (near) continuously monitored path-dependent options, $\tau$ usually takes moderately sized values. In this case, the approximation method described here is advantageous over the double CFTP method in terms of computational complexity (see, e.g., Sections 5.1 and 5.2 and, in particular, Remark 5.3 of \cite{JKZ:2013}).
\end{remark}

\section{SIMULATION STUDIES}\label{sec:numerical}
We investigate the performance of our method in comparison with several widely used simulation methods for simulating option prices. The methods under comparison are those of \cite{PoirotTankov},  \cite{MadanYor}, and \cite{BallottaKyriakou} (hereinafter abbreviated as PT, MY, and BK, respectively),  and the exact method due to \cite{Devroye} (as described in Section \ref{subsec:exactmethodYzeroone}). We abbreviate the version of our time change decomposition method incorporating  double CFTP (see Section \ref{subsec:perfectsimGGC}) as TCD and the version incorporating the approximation scheme (see Section \ref{subsubsec:APPscheme}) as TCD-app.

We consider two simulation settings, namely, the cases of finite and infinite variation, respectively. Table \ref{table:parametersettings} lists the parameter values used in the two simulation designs. In particular, the parameter values for $Y$ are chosen by taking the estimation results from calibrating the model to the option price data, with IBM being the underlying asset in Table 3 on page 327 of \cite{CGMY2002} as reference. As examples, under each simulation design, we consider the pricing of both a European call option (path-independent) and an Asian call option (path-dependent).

\begin{center}
+++ Insert Table \ref{table:parametersettings} about here +++
\end{center}

Under Design I (finite variation), we compare our method with the aforementioned four alternative methods in simulating prices for both a European call option and an Asian call option as described in Section \ref{CGMYintro}. Under Design II (infinite variation), the method of \cite{Devroye} is not included in the comparison, because this method is specifically for the finite-variation case. Both European and Asian call options are also considered under Design II. A risk-free interest rate $r=0.0548$, initial stock price $S(0)=100$, and time to maturity $T=0.25$ (a quarter) are used. For the Asian call option, we set the monitoring frequency $n=13$ (monitored weekly), and the monitoring times are equally spaced. We report simulation results for a strike price $K$ ranging from 80 to 120 with a step size of 10.

The simulation experiments are performed on a desktop PC with an Intel$^\circledR$  Core\texttrademark \ i7-4790 CPU @ 3.60\,GHz 3.60\,GHz and 4.00\,GB RAM. All programs are coded in the C++ programming language and compiled by Microsoft Visual Studio 2010. The reference prices are generated by the (unbiased) method of \cite{PoirotTankov} using $10^{8}$ Monte Carlo trials. The comparison of different methods is based on $10^{5}$ Monte Carlo trials.  The simulation results are summarized in Tables \ref{table:DesignIEuropeanCall}--\ref{table:DesignIIAsianCall}, on the basis of which we make the following comments:
\begin{itemize}
\item Overall, the performance of our proposed time change decomposition method with a moderately sized error bound (i.e., $\varepsilon=\tilde{\varepsilon}=10^{-4}$) is comparable to those of the other methods in terms of the biases of the Monte Carlo price estimates.
\item One would expect our time change decomposition method to give more accurate price estimates if smaller error bounds ($\varepsilon$ and $\tilde{\varepsilon}$) are used, provided that the Monte Carlo error is sufficiently small (i.e., a sufficiently large  number of Monte Carlo trials are used). However, this is only achieved at the expense of increasing computing time.
\item Because we are not pursuing  optimal encoding either of our method or  of the other methods (in fact, we simply adopt the C++ codes for the MY method available on Peter Tankov's personal website\footnotemark\footnotetext{The URL for Peter Tankov's website is: http://www.proba.jussieu.fr/pageperso/tankov/}  and translate the algorithms of the PT and BY methods and that of \cite{Devroye}  straightforwardly into C++), the comparison of the computing speeds among different methods is somewhat ad hoc, although these codes have been implemented in the same computing environment.
\item Although  these simulation experiments  probably do not provide a completely fair comparison of computing speeds among the different methods, it does appear that in general the time change decomposition method is not as efficient as the other methods in this regard.
\item With virtually no loss of accuracy,  time change decomposition with the use of an approximation scheme (TCD-app) allows a large reduction in computing time compared with  time change decomposition  without approximation  (TCD). This result is consistent with the discussion in Section \ref{subsubsec:APPscheme}.
\item Last but not least, we would like to emphasize again that our proposed method allows the most transparent interpretation of the approximation errors involved in the simulation of CGMY increments, which is especially relevant in the infinite-variation case. That is, it is clear that our error bounds ($\varepsilon$ and $\tilde{\varepsilon}$) control the $L^2$ distance between the approximate variate and the target CGMY increment, whereas the errors arising in the other methods under comparison do not have this simple and clear interpretation.
\end{itemize}

\begin{center}
+++ Insert Tables \ref{table:DesignIEuropeanCall}--\ref{table:DesignIIAsianCall} about here +++
\end{center}

\begin{remark}
Although we believe that the differences among the computing complexities of  the different methods will eventually become insignificant as a result of  advances in information technology, a more efficiently designed algorithm for the proposed method is still of practical importance at present. Because an exact path simulation method is not available for CGMY processes of infinite variation, a method that has both transparently interpretable approximation error(s) and an efficiently designed algorithm is desirable. However, as can be seen from Sections \ref{subsec:perfectsimGGC}--\ref{subsubsec:APPscheme}, the construction of a simulation algorithm for our method with uniformly bounded complexity over the whole parameter space is not a straightforward task, and we leave this as a topic for future research.
\end{remark}

\section{CONCLUDING REMARKS}\label{sec:conclusion}
We have found a new and easy-to-implement path simulation method for CGMY processes   with either finite or  infinite variation. Our method is based on a time change representation of the CGMY process and a decomposition of its time change into a \emph{finite} \emph{generalized gamma convolution} subordinator and an independent error term. In the infinite-variation case, in contrast to  the existing path simulation methods of \cite{MadanYor} and \cite{BallottaKyriakou}, which entail nontrivial approximation errors that are difficult to quantify in, say, derivatives pricing applications, our proposed method is more appealing in that its approximation errors have a transparent interpretation, i.e., the error bounds ($\varepsilon$ and $\tilde{\varepsilon}$) in our method control the $L^2$ distance between the approximate variate and the target CGMY increment (see Remark \ref{rem:discLONEerror} and the discussion immediately following (\ref{eq:GHWstoppingN})). Simulation studies on derivatives pricing demonstrate that our method with moderately sized error bounds (namely, $\varepsilon=\tilde{\varepsilon}=10^{-4}$) shows comparable performance to  other methods.

\section{ACKNOWLEDGMENTS}
The idea behind this work originates from a conversation between Professor Lancelot F. James and the second author. Zhiyuan Zhang's research is supported by the National Nature Science Foundation of China (No. 71301097).

redpajama_set_name: RedPajamaArXiv


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David Henry Dewhurst (* 18. August 1945 in Houston, Texas) ist ein US-amerikanischer Politiker. Von 2003 bis 2015 war er Vizegouverneur des Bundesstaates Texas.

Werdegang
Nach der High School studierte David Dewhurst an der University of Arizona. Später betätigte er sich als erfolgreicher Geschäftsmann und Rancher. Er diente als Nachrichtenoffizier in der United States Air Force und arbeitete zeitweise für die CIA sowie das US-Außenministerium. Politisch schloss er sich der Republikanischen Partei an. Zwischen 1999 und 2003 bekleidete er als Nachfolger von Garry Mauro die Position des Texas Land Commissioner, die als Sprungbrett für höhere Ämter gilt.

Im November 2002 wurde Dewhurst an der Seite von Rick Perry zum Vizegouverneur von Texas gewählt. Dieses Amt hat er nach zwei Wiederwahlen seit 2003 inne. Dabei ist er Stellvertreter des Gouverneurs und Vorsitzender des Staatssenats. Im Jahr 2012 bewarb er sich um die Nominierung seiner Partei für die Wahl zum US-Senat, die jedoch an Ted Cruz ging. 2014 strebte er eine weitere Kandidatur für das Amt des Vizegouverneurs an. Dabei unterlag er aber in den Vorwahlen seiner Partei im März des Jahres dem Staatssenator Dan Patrick, der dann im November auch als Stellvertreter des neuen Gouverneurs Greg Abbott gewählt wurde. Damit endete seine Zeit als Vizegouverneur am 20. Januar 2015.

Weblinks

 Biografie beim Senat von Texas
 Ballotpedia

Einzelnachweise

Vizegouverneur (Texas)
Mitglied der Republikanischen Partei
US-Amerikaner
Geboren 1945
Mann
Texas Land Commissioner

redpajama_set_name: RedPajamaWikipedia


text:
The Cornell Daily Sun (https://cornellsun.com/2005/04/05/studios-university-fight-battles-against-illegal-file-sharing/)
Studios, University Fight Battles Against Illegal File Sharing
By | April 5, 2005
Last month, the Supreme Court heard oral arguments in the case of MGM v. Grokster, the record industry's latest attempt to control the uninhibited flow of illegally traded music files over the internet.
Meanwhile, University students continued the illegal exchange of some of the estimated 2.6 billion copyrighted files traded nation-wide each month.
Cornell students partake in file sharing through a variety of means, from the publicly available peer-to-peer (P2P) programs like KaZaA or Limewire, to the somewhat more exclusively offered services provided by websites like www.i2hub.com, that operate by using a program called Direct Connect. In either case, there is clear tension surrounding what constitutes "the appropriate use of protected intellectual property," as Kent Hubbell, dean of students, said in the Cornell Chronicle last July.
At issue in Grokster is whether file sharing program makers can be held liable for secondary copyright infringement — that is, if KaZaA and similar services are responsible for the files exchanged through their programs. MGM, among others in the recording and movie industries, alleges that since the vast majority of information traded among users is illegal, Grokster and other companies are contributing to copyright violations.
Although a major Cornell direct connect hub was shut down after a bootleg video of the Cornell Jon Stewart performance showed up on it, another student, Jae Kwon '05, restarted the file exchange room under a different name. Kwon said a "hub owner doesn't know what files are traded between users."
To counteract the exchange of illegal files, he said, he disconnects users whom he finds sharing copyrighted material.
In contrast to the dark image of file sharing services painted by attorneys for MGM — B. Verrilli, Jr., a lawyer arguing before the Supreme Court, called Grokster "a gigantic machine that was built on infringement" — Kwon credited his hub as "fostering a sense of community among Cornell Resnet users." Regardless of intent, though, Kwon said he is "protected by the Sony Betamax ruling, [a 1984 case at issue in Grokster] as well as the current Grokster v. MGM case."
Just as the issues confronting the campus and the court were similar, so too were the opinions voiced. The root cause of file sharing programs like Direct Connect or Grokster, for instance, was attributed in both venues to a basic desire to escape payment. From the bench of the Supreme Court, Justice David Souter said, "I know perfectly well that I can buy a CD and put it on my iPod. But I also know if I can get music without buying it, I'm going to do so."
Likewise, Rajiv Ravishankar '07 said, "Given the price of CDs today, downloading music seems inevitable. For how easy it is to download a CD online … I don't see the point in paying $15 for music."
The simple fact that music is currently available for free might render the Supreme Court's decision irrelevant: "regardless of the legality of [file sharing] right now, it is still perceived as illegal," said Ben Arfa '08. Since the assumption is that file trading is already an illegal procedure, the Supreme Court's codification of that assumption will, in his mind, have little effect.
There are some indications that the Court's decision might also seek to solve a problem that will ultimately work itself out. Because of recent innovations in legal software, and frequent problems with the software created by companies like Grokster, users may autonomously accept more legal solutions.
Josh Teitelbaum '05 said that "the key is Napster and iTunes … you can charge people a small amount for each song, and people will use these programs if available. College students aren't necessarily going to steal if they don't have to."
Like Arfa, Teitelbaum acknowledged that "what we're doing is illegal," but predicted a change now that legal — and relatively inexpensive — alternatives are available.
In addition, many students have expressed dissatisfaction with Grokster-like services, as these programs are frequently laced with viruses or secondary programs that generate pop-up ads.
"I used to download music from Limewire until my computer began to run more slowly. I was getting pop-ups every couple of minutes," said Chelsea Hall '08.
As the Court's decision in MGM v. Grokster approaches and new techonology becomes available, it is clear that file exchangers are approaching a major crossroads in music downloading. The decision in the case will likely be handed down in June.
Archived article by Rob Fishman
Sun Contributor
Baseball Earns First Ivy Win
By April 6, 2005
In perhaps the most anticipated debut of the spring season, the sun made its inaugural appearance at Hoy Field yesterday, enabling the Cornell baseball team to host its first Ivy League double-header of the season. In the long-awaited home opener against the Yale Bulldogs, the Red fell flat in the first game, dropping an 11-2 decision, before rebounding with a thrilling 4-3 victory in the second contest. "It was great to be in the home opener," said sophomore pitcher Blake Hamilton. "With the nice weather and fan support, it was great to be on the field." With the split, Cornell (5-8, 1-1 Ivy) picked up a little momentum after losing its last four consecutive games over the spring break. Yale (10-10, 1-3 Ivy) now finds itself behind early in the league standings in light of its two close losses to Princeton on Monday. Bulldogs pitcher Josh Sowers spoiled the Red's homecoming in game one, dominating the Cornell lineup throughout his complete-game win. In seven innings of work, the senior right-hander allowed only two runs off six hits, striking out three batters in the process. "Unfortunately, we didn't play very good baseball in the first game," said Cornell head coach Tom Ford. "Yale did a nice job swinging the bat and [Sowers] pitched well." After a scoreless duel with Red starter Tad Bardenwerper over the first three innings, Sowers and his squad put the pieces in motion for Yale's first league victory. The Bulldogs ended the shutout in the fourth inning when a triple by Marc Sawyer scored Zac Bradley from first. Josh Zabar's ensuing double scored Sawyer, and a subsequent double by Matt Stone sent Zabar home and gave Yale a three-run lead. Cornell responded in the bottom of the inning with a solo home run by senior Matt Miller, but the squad was unable to mount much of an offensive threat for the remainder of the game. The Bulldogs buried the Red in an avalanche of offense in the fifth and six innings, scoring three runs and five runs, respectively. After allowing a two-RBI double to Yale's Justin Ankney in the fourth, Bardenwerper was replaced by rookie pitcher Walker Toma. However, Toma fell victim to a string of errors by the Cornell defense in the sixth inning and gave up five additional runs to the Bulldogs — only one of which was earned. Junior second baseman Seth Gordon knocked in the Red's final run of the first game in the bottom of the seventh, but it was of little use in the face of the 10-run deficit. However, the sun truly began to shine down on the Red in the second outing, an intense, 4-3 win requiring ten innings to decide. A pair of freshmen proved to be the critical factor in the extra inning, as rookie Brian Kaufman scored the winning run off a sharp, infield single by classmate Ry Kagan in the bottom of the 10th. "In the second game, we had to grind it out, but finally we came through," Ford said. "We hung in there — this is the type of game we have to win." Things looked grim for the Red after the Bulldogs jumped ahead to a 2-0 lead in the top of the first inning. Sawyer added another RBI to his statistics with a single to the right side and junior John Janco also pounded in a run, forcing Cornell to battle from behind once again. In the second inning, the Red evened the score at two when catcher William Pauly's single scored seniors Matt Miller and Conor Kelly. The following inning gave Cornell its first lead of the series as Kaufman smacked an RBI single to center, his fourth of the season. Overall, Kaufman went 4-for-7, boosting his batting average to .370 in 13 games this season. However, the Red failed to preserve its lead late in the contest, allowing Yale junior Chris Esper to force extra innings with an RBI single to left field in the ninth inning. But Cornell pitcher Jim Hyland was able to shut down the Yale lineup in the 10th and record his first victory of the season. "We made a few mistakes in game one that were hard to recover from because [the mistakes] seemed to compound themselves," Hyland said. "In the second game, we made fewer mistakes. I was happy with the results. Overall, I'll take it." The Red hopes to preserve the momentum from its dramatic victory heading into today's non-conference match up against Binghamton at Hoy Field. "The mark of Tom [Ford]'s teams are that they are just solid," said Yale head coach John Stuper. "They swing the bat well, throw strikes — and that's just what they did in the second game." Following today's double-header, the Red returns to league play over the weekend at Harvard and Dartmouth. Archived article by Kyle SheahenSun Senior Editor
Mets Fans Caught in the Middle of Television Dispute
"I can see Shea Stadium from my roof, but I can't watch a Mets game in my living room? That's just crazy!" opines Andre from Corona, Queens. Yes, it's a difficult time for New York sports fans. Thanks to the squabbling of Time Warner and Cablevision, 2.4 million New Yorkers have been without MSG, Fox Sports Network NY, and Cablevision's other sports networks since March 7. This of course also affects the 350,000 Time Warner subscribers here in upstate New York. While one would normally expect to see the FSN NY and MSG networks on channels 24 and 100, respectively, they have been replaced by College Sports TV and NBA TV while the two parties duke it out. Up until Monday, many of you were probably unaware of the channel pull, because, let's face it, no one really wants to watch the Knicks right now. However, with the start of the baseball season on Sunday, many of you were anxiously waiting to see the new-look Mets play their season opener on Monday against the Reds. Alas, that never transpired. You probably first tuned into ESPN and ESPN2, but there were other games on instead. "Oh, it's probably on MSG," you thought. But wait, NBA TV was there in its place. At this point, you were probably screaming at your television set. You would not be able to see Pedro's and Beltran's first games as members of the Mets. You were going to have to wait to see the highlights on SportsCenter. While you were listened on the radio or constantly updated the score on the Internet, you missed the Mets doing what they do best-losing the game after the bullpen squanders the lead. Now that we're all familiar with the pain that Mets fans are experiencing, let's get to the actual dispute between Time Warner and Cablevision. According to givebackmsg.com, a website run by Cablevision: "MSG has attempted to negotiate a fair and reasonable rights deal with Time Warner Cable for MSG Network and FSN New York. Time Warner Cable has declined the offer to keep games on while the dispute is brought to binding arbitration. Instead, Time Warner Cable has pulled the plug on MSG Network and FSN New York. MSG is still prepared to live by the decision of an independent arbitrator and call[s] on Time Warner Cable to give the fans back their games." Right on, MSG! Fight the good fight! Interested to know more about the "reasonable deal" that MSG had offered, I perused the site for a few minutes, only to find that there was no other information about this deal. Instead, there were only video testimonials from such impassioned Mets fans like Gregg from Queens, who proclaimed that "We deserve to be able to see … the Mets; The Knicks too. I mean, c'mon." Gregg has chosen to invoke the classic "I mean, c'mon," argument, which can be very convincing. However, that wasn't enough for me, so I sought out a different source. According to the New York Daily News, Cablevision wants Time Warner subscribers to pay 30% more per month for FSN NY and MSG. Time Warner refused this increase because no one wants to pay more to watch the Knicks' drive for a lottery pick, and Mets games are not worth nearly as much as Yankees games. Cablevision's offer to settle the dispute via binding arbitration was rejected by Time Warner because the company felt that going to arbitration would only lead to higher prices for its cable subscribers. While each side has been involved in similar disputes in the past (Cablevision with the YES Network in 2002 and Time Warner with Disney in 2000), I can't really in good conscience side with a company that tried to derail New York's Super Bowl and Olympic bids, stop the Jets from getting a West Side stadium, and run the Knicks and the Rangers into the ground. Let's not forget that this whole dispute was probably caused by Time Warner's investment in the new Mets network, which debuts in 2006. With the Mets off of MSG and FSN NY, Cablevision will only have the pitiful Knicks and Rangers to show on its networks. Who is going to pay 30% more per month to watch those games? Not me. While the Mets may have self-destructed on Monday, it would be very ironic if the team completed a huge turnaround this season and made the playoffs when a large portion of its fan base only got to see a third of its games. However, don't despair, dear Mets fans. If you send a copy of this column into DirecTV, you'll get free installation and free HBO for six months, as well as all the Mets game you can handle. If you're still angry at Time Warner for taking away your Knicks and Mets games, you can find solace with fellow Knicks fan Harold from Englewood – "I'm a real diehard Knicks fan. Not being able to see any of the new Knicks and things like that, [not] being able to see Sweetney and all that other stuff, it really makes me mad." Jonathan Auerbach is a Sun Staff Writer. I Never Kid appears alternate Wednesdays. Archived article by Jonathan Auerbach

redpajama_set_name: RedPajamaCommonCrawl


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Houghton Mifflin Harcourt, 9781328585035, 256pp.
Without a strict regimen, Lightly puts the power back in your hands to take control of your life.
Francine Jay pioneered the simple living movement with her best-selling book, The Joy of Less. She has sold more than 300,000 books on simple living, and her advice has been featured in the New York Times, House Beautiful, CNN, BBC, the TODAY show, The Chicago Tribune, El País, Elle España, The Guardian, The Financial Times, Forbes, The Huffington Post, Spiegel, Dr. Oz's The Good Life, Lifehacker, Apartment Therapy, Grist, Consumerist, Reddit, and TreeHugger. The Joy of Less has sold nearly 160,000 copies, is being published worldwide in 21 countries, and was named one of Amazon's Best Books of the Year, Amazon's Best Books of April 2016, and as an Amazon Editors' Pick for Spring 2016.


20 years ago: Beloved Murderer!
In 1992 this Super 8 animation of mine, Beloved Murderer!, was screened at the Frameline Film Festival in San Francisco.
I haven't seen it myself for years, so I'm very glad that it recently was relaunched within the new "Frameline Voices" project which makes over 80 films free and available to wider audiences via YouTube and Vimeo.


I unloaded my staff and purchased the blue one. The blue one isn't usable and I can't find a way to equip my other staff.
When I have the Ice Jade Staff equipped it tells me my skill set doesn't match.
What's the name of the skill set you want to use?
Eternus wrote: When I have the Ice Jade Staff equipped it tells me my skill set doesn't match.
Hey there, post a screenshot if possible so we can see the issue.
As RandomN00b mentions, the skills and weapons need to match up in order for you to use them. For example, if you are equiping a Sword, but you have a Staff skill set, they won't match up. However, this shouldn't stop you from equipping them, it will just mean your skills will be unusable in a fight.
Post some screenshots and we'll see what we can do!
So I think the OP's problem is that he sold is really staff when he purchased the cosmetic one but the cosmetic ice blue staff doesn't equip in hand, it doesn't have any stats or functions as a weapon, just there to look pretty. You need to have a real staff equipped in addition.
Me too... How fix that?????


Fresh from taking a point off the defending champions, Adelaide United midfielder Danielle Colaprico is confident the Reds are ready to make a late season surge in the Westfield W-League.
The Reds drew 1-1 with Melbourne City on Sunday, with keeper Sarah Willacy saving an 89th minute penalty from Kyah Simon to preserve a fantastic result at Lakeside Stadium.
After six rounds, Adelaide is currently in seventh spot on the ladder, five points outside the top four ahead of this week's clash against Melbourne Victory.
"It was great for us to score and come back with a point. The most important thing that we take away from that match is a point away from home," Colaprico said.
"We're still growing as a team and we are showing it through our capabilities, playing behind the line and even in front.
Adelaide produced a great performance to draw with City, despite going behind in the 14th minute through Ashley's Hatch's header.
Alyssa Mautz ensured they would secure a point when she levelled the scores 20 minutes from time.
"The point was great for us, I think it's hard to win on the road and I think a point is what we deserved," Colaprico said.
"I think we played well defensively and showed that we can play at times but we're going to have to clean some things up, and attack also.
Adelaide face Victory at Lakeside Stadium on Saturday, with kick-off at 4.30pm.


text:
Buffalo Grocery Store Mass Shooter Pleads Guilty to Terrorism and Murder Charges
Mon, November 28, 2022 at 4:57 PM
The gunman that killed ten people at a grocery store in a predominantly Black neighborhood in Buffalo, New York, pleaded guilty on Monday to terrorism as a hate crime, murder, and attempted murder.
CNN reports Payton Gendron, 19, pleaded guilty to one count of domestic act of terrorism motivated by hate, 10 counts of first-degree murder, three counts of attempted murder and a weapons possession charge in the May 14 mass shooting at Tops Friendly Market.
The outlet says Gendron said "guilty" while emotionless during the hearing. The guilty plea comes six months after the horrific mass shooting.
Erie County district attorney described the attack as a racist hate crime and outlined the events of that day.
"In just over two minutes, the defendant, with the intent to murder as many African Americans as he could, killed 10 innocent Black people and attempted to kill three others." He used a semiautomatic rifle to kill four people outside of the store then nine others inside.
The attack was proven racially motivated during his live stream. He held the gun up to a White man, then said "sorry" and aimed elsewhere.
It was also revealed that Gendron had planned the attack for months, visiting the Tops supermarket several times to plan his attack. He even admitted that he chose the Tops in the Buffalo area because it had the highest percentage of Black people in the area close to where he lived, Conklin, New York.
His goals of the attack were described as "To kill as many African Americans as possible, avoid dying and spread ideals."
Eleven of the 13 people shot were Black, while two were White.
The defense attorney Brian Parker said:
"This critical step represents a condemnation of the racist ideology that fueled his horrific actions on May 14. Before he is sentenced to life without the possibility of parole on February 15, the surviving victims and deceased victims' family members will all have a chance to address the court, the community and our client directly," he said. "It is our hope that a final resolution of the state charges will help in some small way to keep the focus on the needs of the victims and the community."
The post Buffalo Grocery Store Mass Shooter Pleads Guilty to Terrorism and Murder Charges appeared first on Baller Alert.
via: https://balleralert.com/profiles/blogs/buffalo-grocery-store-mass-shooter-pleads-guilty/
News, Buffalo Grocery Store Mass Shooter Pleads Guilty to Terrorism and Murder Charges
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Dubrovnik to Athens
Experience the seaside charm and Balkan countryside, from Dubrovnik to Athens.
This European adventure combines the must-sees of the Balkan region and the lesser-known glories of North Macedonia and Albania – creating the perfect balance between old and new. Hang out in Dubrovnik's Old Town, cruise around Lake Ohrid, hike the foot hills of Mt Olympus and in Pelister National Park, and sample some regional specialties in Greece's capital. You'll experience the Adriatic coastline and the Balkans interior on a 15-day regional wrap from Dubrovnik to Athens. With a curated selection of inclusions and plenty of free time, this slice of Europe is all yours to explore.
Lock in your 2020 trip with a $1 deposit*. Don't wait. Just go! Offer ends 13 February 2020.
From 23 December 2019 to 13 February 2020, only a $1 deposit will be required to secure your Intrepid Travel trip when travelling by 31 December 2020.
The $1 deposit can be paid towards any Intrepid small group adventure or short break with the following exclusions: Polar trips – includes all itineraries in the Arctic and Antarctic, Tailor-Made Experiences, 18 to 29s Asia Pass, Inca trail and Gorilla permit trips, Charity trips, Expedition style trips, selected Patagonia trips and the Okavango Delta Fly-In Safari (UUAO).
Excluded Gorilla Treks - Pre-purchased permits are required to secure the trek to see the Gorillas. Excluded trips are: YXOG, YXOCC, UXODC, YXOEC, YXOIC, YXOGC, YXOFC, UBODC, YGSU, YGSGC, YGAR, YGAG, YGAU
Excluded Inca Trail trips - Pre-purchased permits are required to secure the trek. Excluded trips are: GGBL, GGBNC, GGBPC, GGBTC, GGBWC, GGBZC, GGCLC, GGCRC, GGHC-O, GGKIC, GGKY, GGOA, GGSA, GGSAC, GGSEC, GGSFC, GGSQ, GGSTC, GGSUC, GGTA, GGTBC, GGXT, GGXTC, GGYP, GGYM, GGYBC, GGYQC, GGYA, GGYC, GGYDC, GGYE, GGYEC, GGYCC
Excluded Select Patagonia trips – Internal flights are pre-purchased to secure the trip: Excluded trips are: GPTV, GPTU, GGCB, GGSJ
The offer can only be applied to new bookings only and cannot be used in conjunction with another offer or discount, the offer is non-combinable. Multiple $1 deposit bookings may not overlap in travel dates, however consecutive $1 deposit bookings are permitted. Full payment is required 56 days prior to departure (90 days prior to departure for Adventure Cruises). If booking within 56 days of departure (90 days prior to departure for Adventure Cruises), full payment is due immediately. Standard booking conditions apply. Cancellation fees apply. All tours are subject to availability. Prices, itineraries and inclusions are subject to change without notice. If the traveller wishes to cancel and rebook or to change dates or tours, they will be required to pay a full deposit towards the new trip. This condition is applicable even inside promotional period.
This offer is valid for residents of Australia and New Zealand booking in AUD or NZD only.
Albania, Croatia, Greece, Macedonia, Montenegro
ZMSM
Admire the World Heritage-listed architecture of Dubrovnik and Montenegro's Kotor, climbing along their ancient city walls.
Loose yourself in Tirana, Albania's colourful capital, and partake in the local's favourite pastime: drinking coffee and people-watching.
Sail across the blue waters of Lake Ohrid – one of Europe's oldest lakes. No wonder North Macedonia and Albania share this beautiful attraction; nobody would want to let it go!
Explore the endemic flora and fauna on an easy hike of Pelister: North Macedonia's oldest national park.
Hike the slopes of Mt Olympus, the ancient seat of the 12 Greek gods. According to mythology Zeus unleashed his thunderbolts from one of Olympus' peaks.
The Balkan peninsula is very hilly and mountainous, so many steps are a feature of the landscape. You will have to be able to easily lift your luggage and carry it up and down stairs and inclines, so packing light is recommended. You may want to consider bringing a backpack instead of a wheelie bag. Also, stone streets become very slippery when wet. Some people may find the Balkan's topography very demanding.
Summer temperatures can be extreme in many of the regions visited (over 40°C), which can be uncomfortable, especially as many of the transport options and accommodations we use will not have air-conditioning. It's important to use sun protection, wear layers to combat the heat and drink plenty of water. Please carefully consider the time of the year you wish to travel and your suitability to that season.
As accommodation on this trip is twin-share, single travellers will share a room with another traveller of the same sex. This trip is a great opportunity to get to know other like-minded people, so embrace it while you can. However, if you'd prefer not to share, a single room supplement is available at an additional charge. Please ask your travel consultant for more details. Hotels in Europe often don't have double beds, but rather two single beds that can be pushed together. Please also note that in some cases bathroom facilities will be shared rather than en-suite, and many accommodations in this part of the world do not have air-conditioning.
Day 1: Dubrovnik
Dobro Dosli! Welcome to Croatia – a place of sunshine, azure waters and charming cobblestone towns. The undisputed jewel of the Dalmatian Coast, Dubrovnik old town is a beautiful white stone town surrounded entirely by city walls, easily covered on foot. Although it experienced devastation during the war in the early 1990s, the restored old town remains as charming as ever. Your adventure begins with a welcome meeting at 6 pm. As there is not much time in Dubrovnik on this trip, you may want to consider arriving one or two days earlier. If you do have time beforehand, why not head out to one of the Elafiti Islands? There's Lopud, a quiet island with lovely hikes, clean beaches and a ruined castle. Kolocep is a sleepy enclave that boasts walks for every fitness level, while Sipan is the most populated of the isles and has the most hospitable locals. There are also many monuments to explore in the city proper, including the 15th century Rector's Palace, monasteries with cloistered gardens, and fine baroque churches with copper domes.
Hostel (1 night)
Franciscan Monastery - HRK30
Dubrovnik - Lokrum Island Boat Trip - HRK150
Dubrovnik - War Photography Museum - HRK50
Game of Thrones Tour - HRK200
Dubrovnik - Rector's Palace - HRK120
Museum of Croatian War of Independence - Mt Srd - HRK30
Church of St. Blaise - Free
Dubrovnik - Hike up Mt Srd - Free
It's very important that you attend the welcome meeting as we will be collecting insurance details and next of kin information at this time. If you are going to be late please let your travel agent or hotel reception know. Ask reception or look for a note in the lobby for more information on where the meeting will take place. If you can't arrange a flight that will have you arrive on time, you may wish to arrive a day early. We'll be happy to organise accommodation for you (subject to availability).
Day 2: Kotor
Leave Dubrovnik behind and take a private transfer to Kotor on the coast of Montenegro (approximately 3 hours). This 5th-century World Heritage-listed city is set on a secluded bay, with towering peaks surrounding a rocky coastline dotted with pretty waterside towns. In its crooked alleyways, get lost and mingle with the locals. When you arrive, why not check out the 12th-century Cathedral, the South Gates, and the Armoury Square? Later, perhaps take a cruise on the Kotor Fjord – the longest fjord south of Scandinavia – and visit an island with a church that's almost as big as the island itself! In the evening the city walls are prettily lit up to provide a unique night-time perspective.
Kotor - Cruise on Kotor Fjord - EUR30
Kotor - Fortress - EUR3
Kotor - St. Tryphon's Cathedral - EUR2
Kotor - Maritime Museum - EUR4
Day 3: Tirana
After breakfast, drive across the border into Albania. A unique mixture of cultures and customs, Tirana is filled with craziness, from its traffic to its nightlife, but on its doorstep are mosques, citadels, Ottoman architecture, and a stunning dose of the medieval Balkans. The real surprise of Albania is the people. Their warmth to strangers is infectious and you're bound to find yourself swapping stories over a glass of raki or three. Our first stop is the city of Shkoder (approximately 3 hours' drive from Kotor). Here you will have time to explore Rozafa Castle. The site was occupied by a fortress since Illyrian times, however most of what can be seen today is of Venetian origin. Depending on road conditions and volume of traffic it will be another 2 hours to Tirana. On arrival, take an orientation walk to get your bearings. Tirana is the capital of Albania and its biggest city, but it's still small and compact, with architectural influences from Italy and Turkey. Recently many buildings have been painted to alleviate the Soviet bloc feeling that pervaded. Many upgrades have been made all over town, such as new parks and wide pavements.
Shkoder - Rozafa Castle
Day 4: Kruja / Tirana
Today, take a half-day trip to the mountain village and former Albanian capital of Kruja. Kruja was the last stronghold of Skanderbeg's (the national hero of Albania) army until the Ottomans took over the entire country. There is plenty of time to explore the citadel and the famous bazaar area. Perhaps pay a visit to the excellent ethnographical museum housed inside the fortress. You'll then return to Tirana after lunch. Tirana is dotted with many museums. You can't miss the National History Museum – just look for the gargantuan mosaic on the facade that represents the development of Albania's history. The main sight in Tirana is the Et'hem Bey Mosque, which sits right on the city's main square. Closed under communist rule, the mosque resumed as a place of worship in 1991. Ten thousand people attended the reopening and the event was considered a milestone in the rebirth of religious freedom in Albania. The mosque is currently undertaking extensive renovation works, but you can still take a look at the frescoes outside and in the portico that depict trees, waterfalls and bridges – motifs rarely seen in Islamic art.
Kruja Day Trip
Kruja Skanderbeg Museum
Kruja - Fortress Visit
Tirana - Sky Tower - ALL400
Tirana - National Art Gallery - ALL200
Tirana - National History Museum - ALL700
Tirana - Bunk'Art Gallery - ALL500
Day 5: Berat
Travel by public bus to Berat, the town of a thousand windows, and one of the few towns of Albania that escaped being razed to the ground to make way for apartment blocks. The old Mangalemi district has recently been inscribed on UNESCO's world heritage list. Enjoy an afternoon guided tour of the town and the looming fortress, the kala, built during the 13th century and still inhabited. The walk to the castle is steep and slippery so better bring some proper footwear with you. The views from the top across Berat and the Osum river valley are well worth the effort though.
Berat - Walking Tour with Local Guide
Berat - Castle Visit
Day 6: Lake Ohrid
Travel by private bus to Ohrid in North Macedonia, a drive of about 3 hours, situated on a lake with the same name. Europe's oldest lake, and one of the oldest human settlements in the world, Ohrid has a wealth of historic sites and religious monuments to discover. Ohrid is an eternal town, a magical hill whose primordial pulsation links ancient and modern times forever. The town is said to have once been home to 365 churches, one for each day of the year, earning it the nickname "the Macedonian Jerusalem", while historical excavations date back to Neolithic times. Despite being a World Heritage site for over 30 years, the town remains off the radar for visitors. Get your bearings on an orientation walk around Ohrid, maybe picking up a bargain or two in the vibrant Old Bazaar. Then embark on a scenic cruise on the turquoise waters of Lake Ohrid, ringed by mountains, attractive villages and beaches, and take in the views of the town and the surrounding scenery while afloat.
Ohrid - Lake Ohrid Boat Cruise
At 34 kilometres long, 14 kilometres wide, and over 300 meters deep, all shared between Albania and North Macedonia, there's plenty of vast Lake Ohrid to explore. Today is free for you to discover the area. There are many churches and monasteries to visit, but one of the most popular is the Macedonian Orthodox Church of Sveti Jovana Kaneo, situated on a rocky outcrop above the town, overlooking the lake. Past the church you can wander around to the back of town, exploring the old walls and fortress, and admiring the views of the lake. The Sveti Naum Monastery is also a great option, lying on the shores of the lake south of town, with well-kept grounds that are home to peacocks. The ancient Tsar Samoil's Fortress stands on the top of Ohrid Hill and looks across the town, while a 2,000-year-old Roman theatre was uncovered near the Upper Gate – in summer it's again being used for concerts and performances.
Ohrid - Robev Family House National Museum - MKD150
Ohrid - St Jovan Church - MKD100
Day 8: Skopje
This morning hop onto public bus to Skopje, North Macedonia's capital city (approximately 3 hours). In Macedonia's political and cultural centre, walk past Byzantine domes, Turkish baths, and also newly built neo-classical buildings and grand monuments (aimed to bolster national pride), sampling gozleme and tasty baklava along the way. The 30 mosques, innumerable caravanserais and hamams that fill its winding streets are a testament to Skopje's Ottoman past. Take a step back to those times with a visit to the Daut Pasha Hamam, or journey through the humbling Holocaust Museum to learn how Macedonia suffered during this tragic chapter of history. Get lost in the narrow lanes of Carsija: Skopje's most atmospheric neighbourhood, or take in the stone bridge over the river Vardar – an iconic sight that acts as a handy connection between Macedonia Square and the Old Bazaar. Perhaps visit the Museum of the City of Skopje, housed in the old Railway Station, which is itself a unique piece of history. Its unusual, part-ruined exterior is a result of the 1963 earthquake. The large clock on the outside of the building is frozen at 5.17 – the moment the earthquake shook the city.
Day 9: Matka Canyon / Skopje
Venture out to Matka Canyon, a deep ravine cut into the Suva mountains by the Treska River, 15 kilometres south-west of the city. This area is home to several medieval monasteries, caves, and over 70 species of butterflies. You could also take up the option to explore the canyon's sights by boat. One of the monasteries worth exploring is St Andrew's Monastery, which contains many superb frescoes of great artistic importance. There is also Vrelo cavern: a water-filled cave with incredible stalagmites and unchartered depths; it's speculated to be the deepest underwater cave in the world. Alternatively, you can take one of the many nature walks in the canyon, or up to tracks that hug the ridge high above the valley. Return back to Skopje, with the remaining part of the day free for you to continue exploring this exciting city. Perhaps take the Mount Vodno cable car to the giant 66-metre high Millennium Cross, mainly for the views back down across the city. For dinner this evening, why not head to the Old Bazaar, or the restaurants in the Debar Maalo area.
Matka Canyon - Day Trip
Matka Canyon Boat Ride - MKD139
Museum of the City of Skopje - Free
Skopje - Kale Fortress - Free
Skopje - Mount Vodno Cable Car to Millennium Cross - MKD100
Skopje - Daut Pasha Hammam - MKD50
Day 10: Pelister National Park / Bitola
Today, continue your adventure with a bus ride to the town of Bitola, located near Pelister National Park. Pelister is North Macedonia's oldest national park covering 171 square kilometres of the Baba massif (type of mountainous geological formation). Eight peaks in this park are over 2000 metres, with Mt Pelister the highest at 2601 metres. Close to the top are two glacial lakes, known as 'Pelister's Eyes'. Today, you'll get the chance to explore the stunning greenery in Pelister on an easy 2-hour hike of the park's lower trails, passing through the lush forests and breathing in the crisp mountain air. Head to the information centre to learn more about the endemic flora and fauna. Return to Bitola for the night.
Hike in Pelister National Park
Day 11: Kastoria
Travel with private transport to the border with Greece and then continue to Kastoria. This medieval town sits on the western shore of Lake Orestiada, in a valley surrounded by limestone mountains. Kastoria is full of interesting Byzantine churches and Ottoman-style architecture, including old distinctive villas from the skin and fur trade times. Once you arrive, take an orientation walk along the labyrinthine lanes, with time to walk along the lakeside, where boats bob, Dalmatian pelicans and ducks make ripples on the water, and coniferous trees and mountains surround in the distance. Later, consider visiting the unspoilt Spilia tou Drakou, or Dragon Cave, one of the most impressive caves in Greece, and see stalactites and underground lakes in this mysterious natural wonder once believed to be a gold mine guarded by a sleepless dragon.
Day 12: Litochoro
Enjoy a free morning in Kastoria. Perhaps visit the Neolithic lakeside village and reconstruction at Dispilio, which gives you a real feel for life in a village in the middle of the 6th millennium BC. After lunch transfer by private vehicle to the town of Litochoro at the base of Mt Olympus. Upon arrival head out on a short orientation walk to familiarise yourself with the surroundings. Head down to the beach at Plaka for some well-deserved relaxation and a dip in the Aegean Sea before tomorrow's hike. Perhaps have dinner in one of the fish tavernas lining the sea shore, and indulge in some traditional dishes.
Guesthouse (1 night)
Day 13: Mt Olympus National Park / Litochoro
Mount Olympus, Greece's first national park, is the highest mountain in Greece and the second highest in the Balkans, with a height of 2918 metres. The mountain is famous in Greek mythology as it is the dwelling of the twelve Olympian gods, headed by Zeus. Mytikas peak was the gods' meeting place, and Stefani peak was the Throne of Zeus from where he was said to have displayed his mighty power by throwing thunderbolts. Head out early today for a hike along a lush trail within the national park to a beautiful waterfall. If it's a hot day, why not brave the cold water? Just don't forget to bring your swimming costume! There is the option to visit the monastery of St Dionysios on the way back into town. The rest of the day is free for you to continue enjoying the surrounding countryside or simply take in the view of the mountain from the vantage point of the nearby beach.
Olympus Orlias Waterfall Hike
Litochoro Agios Dionysios Monastery - Free
Litochoro Plaka Beach - Free
Please note that depending on weather conditions (such as rain or extreme heat), today's activities are subject to alterations or cancellations.
Day 14: Athens
Board a public bus to Athens, the beating heart of Greece, and the centre of the ancient world (approximately 5.5 hours). After arriving and transferring to your central hotel, there's much to be seen in the capital of Greece, vibrant and refreshed following the 2004 Olympics, yet still retaining so much visible history. Named after the goddess of wisdom, Athens has a weighty history that spills out over the modern city, represented most dramatically by the ancient Acropolis, where you can enter the Pantheon and enjoy fabulous views over the city. The birthplace of Western civilisation, Athens has an amazing array of historic sites to explore, including the National Gardens, the Temple of Olympian Zeus and the original Olympic Stadium. Another highlight is the renowned changing of the guard at Syntagma (Parliament) Square. Afterwards, perhaps tuck into a delicious dinner of Greek cuisine and a shot (or two) of ouzo.
Numismatic Museum - EUR6
National Archaeological Museum - EUR10
Lycabettus Hill - Free
Acropolis Pass for 5 Sites - EUR30
Dora Stratou - EUR15
There are no activities planned for today and you are able to depart the accommodation at any time. As there is so much to see and do in Greece's capital you may want to extend your stay here. We'll happy to assist with additional accommodation (subject to availability).
Urban Adventures - Walking Athens - EUR55
Urban Adventures - Taste of Athens - EUR68
Urban Adventures - Markets, Ruins & Ancient Athens - EUR58
Urban Adventures - Twilight Athens - EUR91
Urban Adventures - Bohemian Tales of the City - EUR70
Day Trip to Delphi - EUR60
If you haven't had enough of Greece yet why not join our connecting Greek Islands trip, taking in the best of the islands in the Aegean Sea, such as Mykonos and Santorini. Most departure dates are designed to create this perfect combination trip. Or, if you have some extra time in Athens, you can take one of the day trips offered by Urban Adventures. Check out urbanadventures.com for more information.
14 breakfasts
Public bus, Private vehicle, Taxi, Boat
Hotel (10 nights), Guesthouse (2 nights), Homestay (1 night), Hostel (1 night)
There are currently no scheduled departures on our Dubrovnik to Athens trip. If you are interested in other trips in the region visit one of the links below.
Dubrovnik to Santorini
Soak up the diverse Mediterranean on a trip through Croatia, Albania, Montenegro and...
SINGLE SUPPLEMENT
A single supplement is bookable on this trip, subject to availability at the time of booking. Please note that due to the small properties we use in Europe there is only a limited amount of single supplements available per trip departure. If you would like to book a single supplement and enquire about availability please speak to your booking agent.
There is not much time in Dubrovnik on this trip, so you may want to consider arriving a few days earlier to make sure you are not missing out on everything that this beautiful city has to offer.
As an Australian-owned business, we acknowledge the Traditional Owners of Country throughout Australia and their continuing connection to land, waters and community. We pay our respects to them and their cultures, and to their Elders past, present and future.
Call us 24/7 on 1300 797 010 or send us your enquiry below


text:
Sales Down 6.4% For Tesco Ireland In H1
October 23, 2014 8:16 AM By square1
Tesco's Irish operation saw its like-for-like sales drop by 6.4 per cent (excluding petrol) in the first half of its financial year, according to results filed this morning.
Following a full-year decline of 5.5 per cent in 2013/14, Tesco Ireland saw like-for-like sales drop 5.5 per cent year on year in Q1 of 2014/15 and 7.3 per cent in Q2.
Overall, total sales for Tesco's European operations declined 1.8 per cent at constant rates.
"The pressure on sales, particularly in Ireland and Slovakia, held back any further profit growth," Tesco said in a statement. "The Irish market remained challenging, with intense competition led by the discounters and high levels of coupling."
The period saw the introduction of the Delivery Saver scheme in Ireland for online orders.
Commenting on the retailer's disappointing international performance, David Gray, retail analyst at Planet Retail, said, "Even the international business, once Tesco's dependable wingman in a tight spot, is showing less heart for the fight."


There is something in Veronica Roth's writing that I connect to. I love seeing the way her characters wrestle with questions of morality, ethics, and habits--and where the three intersect. I love seeing the ways in which they find strength and the ways in which they still feel weak. Such was the case with the Divergent trilogy, and such was also the case with her latest book (which starts a new, separate series), Carve the Mark.
That is, the types of things that I enjoyed in her writing I also found in this new book, but it was not simply a repeat of Divergent. These characters, for one, are in a completely different setting. This type we're in a galaxy of planets, each with their own culture and way of doing things. Everything is set up well, and I immediacy had a sense of a unique, lived-in environment. I liked the environment of Divergent; I like this one just as much, if not more, and it has even more detail to it because it does involve more cultures and planets.
I also love the two main characters, Akos and Cyra. They're just fascinating to watch, and their personal struggles highlight so many of the questions that we all come across as we go about our lives. Questions of weakness, of strength, of duty, of honor, of loyalty, of tradition, of home, of loss, of right and wrong, of revenge versus justice. This way of analyzing morality (if that's the best word to use here) that Veronica Roth has just draws in my attention and doesn't let go.
She is also good at portraying groups of people, while at the same time giving the very personal perspectives of just a couple of characters. We have the closest look at the two main characters and we really get to know how their minds work, but we also have a good look at the people who surround them. Friends, foes, casual acquaintances, family, etc. There is always a sense that these people are all pieces that come together to make a whole.
And that talent of portraying groups, of course, goes well with one the main themes of this book: the importance of every individual. That's why you carve the mark. But I won't explain what that means: if you've read the book, you already know. And I don't want to talk about plot details in this post.
I suppose that means that this is all, then. For me, Carve the Mark was just a very good read. Exciting and suspenseful at times, but more than that, its lasting value was in its characters and the questions that they ask of themselves and the conclusions that they arrive at. I am much looking forward to the sequel, but in the meantime I'm just enjoying what this book offered.


Arte Bar, launched by Americans Alisa Rosseter and Bruce Anderson in February of 2017 is quickly becoming a local sensation. The studio situated in the Eixample neighborhood offers no-experience-required painting and wine nights. Prior to moving to Barcelona, Bruce and Alisa had organized fine art summer camps in the US, France and in nearby Girona.
All painting supplies are at the ready; including the acrylic paint, canvas, brushes and even hairdryers to help dry the paint faster. The professional instruction, local wine, craft beer and tasty nibbles are also included in the price of €27 per person, (plus IVA).
Bruce, a talented and experienced artist, guides you through a set painting study step by step. Alisa offers constructive advise and masterfully orchestrates the event, leaving no palette dry or wine glass empty. The atmosphere is geared towards fun and open creativity and there is no pressure to follow a set of rules. Best of all, at the end of the evening you can take your freshly minted masterpiece home with you.
The events last between two and three hours and also have an important social aspect. During the session there are breaks where you can chat and get to know like minded creative people – both Barcelona locals and visitors passing through town.


Washington, D.C. (December 12, 2016) — The Human Animal Bond Research Initiative (HABRI) and the Pet Care Trust announced today they had awarded a combined $130,000 grant to American Humane, for a study titled, Pets in the Classroom (PIC): What are the Social, Behavioral, and Academic Effects of Classroom Pets for Children, 8-10 years? It is hypothesized that students with a classroom pet will experience increased social skills, improved academic competence and decreased competing problem behaviors compared to students who do not have a classroom pet.
The first phase of the PIC Study concluded in May 2015 and was supported by The Pet Care Trust, which operates the popular Pets in the Classroom grant program. The first phase consisted of surveying and interviewing teachers on their perspectives regarding the main benefits, challenges and uses of their classroom pets, which ranged from fish to guinea pigs, hamsters, bearded dragons, and others. This second phase of the study will examine approximately 650 students and parents, as well as 46 teachers from 23 U.S. third and fourth grade classrooms over the course of a nine-month school year. Students, teachers, and parents will complete questionnaires at three times throughout the study period to measure the social, behavioral, and academic effects of classroom pets and human-animal relationships on children.
The HABRI Foundation maintains the world's largest online library of human-animal bond research and information; to date has funded more than $750,000 dollars in innovative research projects to scientifically document the health benefits of companion animals; and informs the public about human-animal bond research and the beneficial role of companion animals in society. For more information about the HABRI Foundation, visit habri.org.
Incorporated in 1990, The Pet Care Trust is a non-profit, charitable, public foundation whose mission is to help promote public understanding of the joys and benefits of pets through education, support, and interaction, and to enhance knowledge about companion animals through research and education. To learn more about the Trust, visit www.petsintheclassroom.org/about.
Founded in 1877, American Humane is committed to ensuring the safety, welfare and well-being of animals. Our leadership programs are first to serve in promoting and nurturing the bonds between animals and humans. For more information, please visit www.americanhumane.org.


Loyola University Chicago is a private co-educational Jesuit university established in Chicago in 1870 as Saint Ignatius College. It was founded by the Roman Catholic religious order of the Society of Jesus and bears the name of the Jesuit patron, Saint Ignatius of Loyola. Loyola is one of twenty-eight member institutions of the Association of Jesuit Colleges and Universities and, with its current enrollment of more than 15,500 students, is the largest Jesuit University in the United States. Loyola is considered one of the 262 "national universities" by U.S. News & World Report. Loyola's part-time Graduate School of Business has been ranked in the top 10 by U.S. News & World Report, and the University as a whole was ranked the 50th best value in the country. Business Week also ranked Loyola's Graduate School of Business 8th in the nation for its intensive Part-Time MBA program. In addition, Loyola University Chicago is ranked "tier 1" among the nation's top universities according to official USNews.com rankings.
Question and Answer about "Loyola University Chicago"


text:
Dermatology > Skin Cancer
Second Primary Melanoma Increases Risk for Death
— Data a reminder of the importance of regular skin exams
by Leah Lawrence, Contributing Writer, MedPage Today June 27, 2019
Overall survival for patients with multiple primary melanomas was 31% worse compared to those with a single primary melanoma, a retrospective study from the Netherlands found.
Looking at data from close to 57,000 patients from the nation's cancer registries, 36.8% of these second primaries were found within the first year of an initial diagnosis while 27.3% were found after 5 years of follow-up, reported Mary-Ann El Sharouni, MD, and colleagues from University Medical Center Utrecht in the Netherlands.
"The findings suggest that current melanoma follow-up strategies need to be reconsidered for patients with multiple primary melanomas and guidelines should comment on this," they wrote in JAMA Dermatology.
The retrospective study looked at adults with primary, invasive cutaneous melanoma diagnosed in the Netherlands from 2000 to 2014, with a median follow-up of 75.1 months.
The survival analysis compared data from 1,767 multiple primary and 37,049 single primary melanomas. Corrected for all variables, the hazard ratio for death was 1.31 for those with multiple primaries (95% CI 1.20-1.42, P<0.001).
Presence of ulceration (HR 2.20), Breslow thickness (HR 1.11 per mm), and increasing age (HR 1.06 per year) were all significantly associated with worse survival for these patients.
"Because patients with multiple primary melanomas had worse survival than patients with a single primary melanoma in our multivariable analysis, we believe that a patient, once proven to have developed a second melanoma, may benefit from more thorough surveillance," El Sharouni's group wrote.
Having one melanoma increases a person's risk for having another, Jennifer Stein, MD, PhD, associate professor of dermatology at NYU Langone Health in New York City, told MedPage Today.
"The second melanoma can occur anywhere on the body and can develop in a completely different part of the body from the first melanoma," Stein said, noting that if found early it is completely curable.
In addition to the finding of increased risk for death among those with more than one melanoma, another important finding was that the additional melanomas were usually thinner than the original melanoma, said Stein, who was not involved in the study.
The researchers found a significant decrease in median Breslow thickness from first melanoma to subsequent melanomas (0.90 vs 0.65 mm, P<0.001), a finding that suggests increased dermatologic surveillance after the primary diagnosis, they noted.
"Thinner melanomas are less likely to spread to other parts of the body than thicker melanomas, so it is important to find melanomas early, when they are as thin as possible," Stein said. "This article reminds us of the importance of regular skin exams for patients who have had melanoma."
In the overall study cohort (N=56,929), there were 54,645 single primary melanomas and 4,967 multiple primary melanomas (from 2,284 patients).
The incidence of multiple primary melanomas was 4%, with men more likely to have multiple primaries than women (49.6% vs 43.7%, P<0.001).
About half of second melanomas (48.7%) had the same T stage as the primary diagnosis -- 16.2% had a higher T stage, and 35.1% had a lower T stage (P<0.001).
Leah Lawrence is a freelance health writer and editor based in Delaware.
El Sharouni and colleagues reported no conflicts of interest.
Stein reported no conflicts of interest.
JAMA Dermatology
Source Reference: El Sharouni MA, et al "Comparison of survival between patients with single vs multiple primary cutaneous melanomas" JAMA Dermatol 2019; DOI: 10.1001/jamadermatol.2019.1134.