The Optimization Analysis And Robust Modeling Of Multi-stage Portfolio Problem

This paper mainly focuses on the multi-stage portfolio problem, which is modeling as a stochastic programming since some parameters were regarded as stochastic. The first part of this paper is the optimization analysis of the multi-stage portfolio problem. We assume that the investor wants to do a T-stages investment on n securities, and the problem is that the investor wants to tell whether one whole portfolio selection is better than some portfolio selections. We added a constraint to the multi-stage portfolio problem and modeled it as a two-stage model with recourse. Then we regarded the securities as players in a game to construct a cooperative game. In the end, with the help of the duality of stochastic programming, we proved that the core of this game is nonempty, which demonstrates that the investor should choose all the securities to create just one multi-stage portfolio selection. In the second part of the paper, we discussed the fact that the optimal solution to the classical mean-variance model is sensitive to the sample mean. That is to say, the model is not robust. We tried to model a multi-stage portfolio selection with the help of the definition of robustness. It is very difficult to solve a stochastic programming with traditional approaches. In this paper, we use the robust optimization approach successfully turn the stochastic linear constraint into a stochastic programming to some secondary order cone programming which is easy to solve relatively. In the end, we choose an example to prove the computing tractability of the robustness approach.