Abstract: This study discusses optimal asset allocation strategy of a utility-maximizing investor dynamic in time as new market information becomes available to the investor. The objective is to find the optimal strategy that maximizes the expected total discounted log-utility of consumption over finite life time. Trading is assumed to take place between stock and risk-free bond (money account) paying constant interest rate. The underlying uncertainty in the stock price is governed by binomial process based on simple Markov chain approximation of diffusion process. The problem is solved using stochastic dynamic programming approach. In contrast to the continuous-time counterpart, the optimal trading and consumption 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. The result is then applied to Indonesia’s stock data.