Statistical Arbitrage Opportunities Using Bellman Equation

This paper uses the dynamic programming to detect the optimal statistical arbitrage opportunities in a market including a bond and a stock. First, it is assumed that the growth rates of stock are independent random variables and Bellman equation is derived for probability of gain of a portfolio containing a long position in stock and short position in bond. The Bellman equation is derived and its approximations are studied. Then, using the simulation, the performance of method in correlated growth rates cases is proposed. Conclusions are also given.