Dynamic Portfolio Optimization for Utility-Based Models

Portfolio management deals with the allocation of wealth among different investment opportunities, considering investor's preferences on risk. In this paper we consider a multiperiod model where the investor rebalances a portfolio at the beginning of each period facing uncertainty associated with the prices of the assets at future dates. Models of this decision problem tend to become very large because of the dynamic structure and uncertainty. We present a multiple period portfolio model over a finite horizon with transaction costs, a risk averse utility function and the uncertainty modeled using the scenario approach. We propose a new method for efficiently solving real problems; the procedure utilizes stochastic programming combined with decomposition and approximating techniques. Solving the resulting optimization problem relies on approximate dynamic programming techniques. The technique used for solving the portfolio problem provides a method whose effectiveness is proved by the experimental results.