Risk premium is one of main concepts in mathematical finance. It is a measure of the trade-offs investors make between return and risk and is defined by the excess return over the risk-free interest rate earned per one unit of risk of an asset . The purpose of this article is to find the upper and lower bounds of the risk premium of an asset based on the  prices of options in the market . One of  key assumptions to achieve this  is that the market is Markovian. Under this assumption, we can transform the problem into a problem of a second-order differential equation and then obtain the upper and lower bounds  by analyzing the differential equation.
The risk premium is one of main concepts in mathematical finance. It is a measure of the trade-offs investors make between return and risk and is defined by the excess return relative to the risk-free interest rate that is earned from an asset per one unit of risk . The purpose of this article is to determine upper and lower bounds on the risk premium of an asset based on the market prices of options . One of the key assumptions to achieve this goal is that the market is Markovian. Under this assumption, we can transform the problem of finding the bounds into a second-order differential equation . We then obtain upper and lower bounds on the risk premium by analyzing the differential equation.
R
Risk
The risk
R
over
relative to
R
earned
that is earned from an asset
D
of an asset
R
find the
determine
R
of
on
A
market
D
in the market
A
the
A
goal
R
into a problem of a
of finding the bounds into a
R
and then obtain the
. We then obtain
A
on the risk premium