A stochastic linear goal programming approach to multistage portfolio management based on scenario generation via linear programming

Abstract

A stochastic linear goal programming model for multistage portfolio management is proposed. The model takes into account both the investment goal and risk control at each stage. A scenario generation method is proposed that acts as the basis of the portfolio management model. In particular, by matching the moments and fitting the descriptive features of the asset returns, a linear programming model is used to generate the single-stage scenarios. Scenarios for multistage portfolio management are generated by incorporating this single-stage method with the time-series model for the asset returns. Meanwhile, no arbitrage opportunity exists in the proposed method. A real case is solved via the goal programming model and the scenario generation approach which demonstrates the effectiveness of the model. We also comment on some practical issues of the approach.