Utility Based Portfolio Optimization through Integer Programming Under Stochastic Markets

Optimization of a portfolio based on utility functions has been a long line of research in the past. In practice, the solutions discussed earlier are approximated to integers, because of the availability of stocks in integer units. But utility functions are quite sensitive to the amounts invested. Thus mere approximations may lead to loss in utility. In this paper, a procedure called the Integer solution to Expected Utility Maximization (ISEUM) is suggested, where the investor can obtain a pure integer solution to the portfolio optimization problem. This is discussed under the assumption of stochastic markets, where the market states follow a Markov chain. Illustrations showing three different types of investors are presented and the corresponding optimal integer solution is obtained for each market state. In each case, solutions based on the ISEUM procedure are compared with non-integer and corresponding approximated solutions. The loss due to approximation is assessed for each case.