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中文摘要：
本文在不确定退出时间和随机市场环境下利用拉格朗日对偶方法研究了多阶段均值-方差投资组合选择问题.我们假定市场上的资产全是风险资产,且随机市场环境只有有限个自然状态,自然状态的转移过程为时变马尔可夫链,各阶段资产的随机收益率不仅与时间有关而且与市场所处的状态有关.首先利用动态规划技术和拉格朗日对偶方法得到了模型的有效投资策略及有效边界的显式表达式.然后,还给出并证明了一个多阶段版本的两基金分离定理,最后,为说明本文的结论及应用,给出了一个数值算例.
英文摘要：
Using Lagrange duality method, this paper investigates a multi-period mean-variance portfolio selection problem under uncertain exit time and stochastic market environment. We assume that all the assets in the market are risky, and there are only a finite number of states in the market and the state transition process follows a time varying Markov chain, and the random returns of the assets over every period not only depend on the time but also depend on the market state. Firstly, by using the dynamic programming technique and the Lagrange duality method, we obtain the explicit expressions for the efficient investment strategy and the efficient frontier. Then, we provide and prove a multi-period version of two fund separation theorem. Finally, a numerical example is presented to illustrate the results obtained in this paper.
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