Optimal portfolio in discrete-time under HARA utility function

In this study we are going to discuss about optimal dynamic portfolio strategy given the new information of the market to the investor. The objective is to find the optimal strategy that maximizes the expected total hyperbolic absolute risk aversion (HARA)-utility of investor weight portfolio over finite life time. There are two assets that take place in to the dynamic portfolio model, risky asset and risk-free bond with constant interest rate. The underlying stock price is obtained under binomial process of Markov chain approximation of diffusion process. The stochastic dynamic programming is used as the approach to solve the problem. In contrast to the continuous-time counterpart, the optimal trading strategies are found to be time-dependent in recursive manners. Sufficient conditions for short selling are given in terms of physical and martingale probabilities of the stock price.