Portfolio selection using multistage stochastic programming

This paper shows how a mean-variance criterion can be applied to a multi-period setting to obtain efficient portfolios. In order to represent the stochastic and dynamic characteristics necessary for modelling (autocorrelated) returns, a process of asset returns is discretized with respect to time and space and summarized in a scenario tree. Wealth evolves according to the realized returns and the chosen rebalancing strategy by obeying budget equations, which take transaction costs and a riskless asset into consideration. The resulting optimization problem is solved by means of stochastic multistage programming. Furthermore, instead of minimizing the multi-period variance we may maximize quadratic utility of final wealth leading to the same set of optimal portfolios.