| 借贷利率限制下资产-负债管理问题的均值-方差模型 |
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| 引用本文： | 常浩,常凯.借贷利率限制下资产-负债管理问题的均值-方差模型[J].数学的实践与认识,2012,42(18):52-62. |
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| 作者姓名： | 常浩 常凯 |
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| 作者单位： | 1. 天津工业大学数学系,天津300387;天津大学管理学院,天津300072
2. 哈尔滨工业大学深圳研究生院,深圳,518055 |
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| 基金项目： | 教育部人文社会科学研究青年基金，天津市高等学校科技发展基金 |
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| 摘 要： | 将负债过程和借款利率限制引入投资组合优化问题中,并建立该问题的均值-方差模型.通过引入拉格朗日函数并应用拉格朗日对偶定理得到一个等价的新的优化模型,然后应用动态规划原理得到了最优投资策略和有效前沿的解析表达式.算例解释了所得结论.
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| 关 键 词： | 借贷利率 资产-负债问题 均值-方差模型 动态规划 最优投资组合 有效前沿 |
Mean-Variance Model for Asset and Liability Management Problem with Borrowing Constraint |
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| CHANG Hao
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CHANG Kai.Mean-Variance Model for Asset and Liability Management Problem with Borrowing Constraint[J].Mathematics in Practice and Theory,2012,42(18):52-62. |
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| Authors: | CHANG Hao CHANG Kai |
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| Institution: | 1.Department of Mathematics,Tianjin Polytechnic University,Tianjin 300387,China) (2.School of Management,Tianjin University,Tianjin 300072,China) (3.Shenzhen Graduate School,Harbin Institute of Technology,Shenzhen 518055,China) |
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| Abstract: | This paper introduces liability process and borrowing constraint into portfolio optimization problem and formulates this problem in a continuous-time mean-variance framework.By introducing Lagrange function and applying Lagrange duality theorem,we obtain a newly equivalent objective function.Explicit closed-form solutions to the optimal investment strategy and efficient frontier are derived.The results obtained are illustrated on a numerical example. |
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| Keywords: | different interest rates for borrowing and lending asset and liability management mean-variance model dynamic programming optimal portfolio efficient frontier |
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