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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.
In this paper, Lagrange’s duality method is used to study the multi-stage mean-variance portfolio selection under uncertain exit time and stochastic market conditions.We assume that the assets in the market are all risky assets and the stochastic market environment has only a limited number of natural states , The transition of the natural state is a time-varying Markov chain, the stochastic rate of return of assets in each stage is not only related with the time but also with the state of the market.Firstly, the dynamic programming technique and Lagrange’s dual method are used to get the model An effective investment strategy and an explicit boundary of the effective boundary.And then, a multi-stage version of the two-fund separation theorem is also given and proved. Finally, a numerical example is given to illustrate the conclusion and application of this paper.