  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.
