Worst-case Decisions For Multi-period Mean-variance Portfolio Selection And Its Application

Everyone in the economics have to face the uncertain factors and their affects, the result of his action is determined by both certain factors and uncertain factors. Theories that help people solve the certain problem are nearly perfect, but until now, we still find it hard to solve the uncertain problems. But in most decision making problem we have to face uncertain factors, so how to treat the uncertainties and how to select the optimum decision is very important.The main purpose of this paper is how to select the assets and allocate the funds when the worst case (highest risk) realize. Based on the scenario tree generation, the scenario is used to represent a discretised estimate of return uncertainties and associated probabilities in future stages, we proposed a worst-case robust decisions for multi-period mean-variance portfolio optimization framework with the consideration of riskless security. Both the transaction costs and the box constraints are considered in the application.The paper is organized as follows. Section 1 is introduction, the background, the purport the contents and the measures of the research are introduced. And generally list the construction of this paper. Section 2 summarizes the associated theory:modern portfolio theory, robust optimization theory and the scenario tree generation theory. In Section 3, we introduce multi-period discrete min-max formulations of multi-period mean-variance optimization problem for robust, optimal investment strategies in view of rival return and risk scenarios (which are input scenarios in the min-max formulation). Section 4, worst-case robust decisions for multi-period mean-variance portfolio optimization framework with the consideration of riskless security is proposed. In Section 5, we applied these frameworks to the Chinese security market, obtain the multistage dynamic invest strategy, and compare the difference between them. And the sixth section is the conclusion and point out the problems to study further.