A mixed integer programming model for multistage mean–variance post-tax optimization

In this paper, we introduce a mixed integer stochastic programming approach to mean–variance post-tax portfolio management. This approach takes into account of risk in a multistage setting and allows general withdrawals from original capital. The uncertainty on asset returns is specified as a scenario tree. The risk across scenarios is addressed using the probabilistic approach of classical stochastic programming. The tax rules are used with stochastic linear and mixed integer quadratic programming models to compute an overall tax and return-risk efficient multistage portfolio. The incorporation of the risk term in the model provides robustness and leads to diversification over wrappers and assets within each wrapper. General withdrawals and risk aversion have an impact on the distribution of assets among wrappers. Computational results are presented using a study with different scenario trees in order to show the performance of these models.