系统工程理论与实践
繫統工程理論與實踐
계통공정이론여실천
Systems Engineering—Theory & Practice
2014年
11期
2737~2747
,共null页
不确定退出时间 随机市场环境 拉格朗日对偶方法 两基金分离定理 有效边界
不確定退齣時間 隨機市場環境 拉格朗日對偶方法 兩基金分離定理 有效邊界
불학정퇴출시간 수궤시장배경 랍격랑일대우방법 량기금분리정리 유효변계
uncertain exit time; stochastic market environment; Lagrange duality method; two fundseparation theorem; efficient frontier
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.
本文在不確定退齣時間和隨機市場環境下利用拉格朗日對偶方法研究瞭多階段均值-方差投資組閤選擇問題.我們假定市場上的資產全是風險資產,且隨機市場環境隻有有限箇自然狀態,自然狀態的轉移過程為時變馬爾可伕鏈,各階段資產的隨機收益率不僅與時間有關而且與市場所處的狀態有關.首先利用動態規劃技術和拉格朗日對偶方法得到瞭模型的有效投資策略及有效邊界的顯式錶達式.然後,還給齣併證明瞭一箇多階段版本的兩基金分離定理,最後,為說明本文的結論及應用,給齣瞭一箇數值算例.
본문재불학정퇴출시간화수궤시장배경하이용랍격랑일대우방법연구료다계단균치-방차투자조합선택문제.아문가정시장상적자산전시풍험자산,차수궤시장배경지유유한개자연상태,자연상태적전이과정위시변마이가부련,각계단자산적수궤수익솔불부여시간유관이차여시장소처적상태유관.수선이용동태규화기술화랍격랑일대우방법득도료모형적유효투자책략급유효변계적현식표체식.연후,환급출병증명료일개다계단판본적량기금분리정리,최후,위설명본문적결론급응용,급출료일개수치산례.
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.
