Dynamic stochastic programming for asset allocation problem

Asset allocation is an important decision problem in financial planning. In this paper, we study the multistage dynamic asset allocation problem which an investor is allowed to reallocate its wealth among a set of assets over finite discrete decision points, in which the stochastic return rates of the assets follow a Markov chain with nonstationary transition probabilities. The objective is to maximize the utility of the wealth at the end of the planning horizon where the utility of the wealth follows a general piecewise linear and concave function. Transaction costs are considered. We formulate the problem with a dynamic stochastic programming model and develop a method that decomposes the problem into stage-based subproblems to solve it. The main advantage of this method is that it provides a computationally tractable tool to deal with the dynamic asset allocation problem of long planning horizon.