Dynamic Portfolio Optimization in Discrete-Time with Transaction Costs

A discrete-time model of portfolio optimization is studied under the effects of proportional transaction costs. A general class of underlying probability distributions is assumed for the returns of the asset prices. An investor with an exponential utility function seeks to maximize the utility of terminal wealth by determining the optimal investment strategy at the start of each time step. Dynamic programming is used to derive an algorithm for computing the optimal value function and optimal boundaries of the no-transaction region at each time step. In the limit of small transaction costs, perturbation analysis is applied to obtain the optimal value function and optimal boundaries at any time step in the rebalancing of the portfolio.