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
5期
1089~1099
,共null页
不确定终止时间 通货膨胀 均值-方差模型 最优投资策略 Hamilton—Jacobi—Bellman方程
不確定終止時間 通貨膨脹 均值-方差模型 最優投資策略 Hamilton—Jacobi—Bellman方程
불학정종지시간 통화팽창 균치-방차모형 최우투자책략 Hamilton—Jacobi—Bellman방정
uncertain time-horizon; inflation; mean-variance model; optimal investment strategy; Hamilton-Jacobi-Bellman equation
本文基于连续时间均值一方差框架，研究了通货膨胀影响下投资终止时间不确定的最优投资组合选择问题．与以往大多数文献不同，本文所考虑的金融市场仅存在风险资产．首先构建了含通货膨胀及终止时间不确定因素的风险资产均值．方差投资组合选择模型．然后利用随机动态规划方法和Lagrange对偶原理得到了有效投资策略及有效边界的解析表达式，并进一步讨论了本文模型的几种特殊情形．最后，通过数值算例对本文所得结论进行阐述．
本文基于連續時間均值一方差框架，研究瞭通貨膨脹影響下投資終止時間不確定的最優投資組閤選擇問題．與以往大多數文獻不同，本文所攷慮的金融市場僅存在風險資產．首先構建瞭含通貨膨脹及終止時間不確定因素的風險資產均值．方差投資組閤選擇模型．然後利用隨機動態規劃方法和Lagrange對偶原理得到瞭有效投資策略及有效邊界的解析錶達式，併進一步討論瞭本文模型的幾種特殊情形．最後，通過數值算例對本文所得結論進行闡述．
본문기우련속시간균치일방차광가，연구료통화팽창영향하투자종지시간불학정적최우투자조합선택문제．여이왕대다수문헌불동，본문소고필적금융시장부존재풍험자산．수선구건료함통화팽창급종지시간불학정인소적풍험자산균치．방차투자조합선택모형．연후이용수궤동태규화방법화Lagrange대우원리득도료유효투자책략급유효변계적해석표체식，병진일보토론료본문모형적궤충특수정형．최후，통과수치산례대본문소득결론진행천술．
Based on a continuous-time mean-variance model, this paper considers a portfolio selection problem under inflation when time-horizon is uncertain. Different from most of the existing literature, the financial market considered in this paper consists of only risky assets. First of all, incorporating the uncertain factors of inflation and uncertain time-horizon, a mean-variance portfolio selection model with only risky assets is constructed. Second, closed-form expressions for efficient investment strategy and efficient frontier are derived by employing stochastic dynamic programming and Lagrange dual principle. Third, some special cases are discussed. Finally, a numerical example is provided to illustrate the results obtained in this paper.
