最小收益约束下的最优投资问题

华南理工大学学报（自然科学版） ›› 2005, Vol. 33 ›› Issue (3): 95-98,102.

最小收益约束下的最优投资问题

何春雄罗军涂钰青焦健

华南理工大学数学科学学院，广东广州 510640

收稿日期:2004-06-02 出版日期:2005-03-25 发布日期:2005-03-25
通信作者: 何春雄(1958-)，男，教授，主要从事随机分析和金融数学研究 E-mail:maehxhe@scut.edu.cn
作者简介:何春雄(1958-)，男，教授，主要从事随机分析和金融数学研究

Optimal Investment Problem Under M inimum Return C0Ilstraint

He Chun-xiong Luo Jun Tu Yu-qing Jiao Jian

College of Mathematical Sciences，South China Univ.of Tech.,Guangzhou 510640, Guangdong,China

Received:2004-06-02 Online:2005-03-25 Published:2005-03-25
Contact: 何春雄(1958-)，男，教授，主要从事随机分析和金融数学研究 E-mail:maehxhe@scut.edu.cn
About author:何春雄(1958-)，男，教授，主要从事随机分析和金融数学研究

摘要/Abstract

摘要： 在最优投资问题的约束条件为收益不低于市场组合收益(随机收益)与固定保本收益最大者的情况下，采用Black—Scholes期权定价框架，构造等价鞅测度求解得到该优化问题的最优投资策略，同时在HARA效用函数下分析该投资问题的性质，发现在不同条件下，该投资策略可以退化为无约束最优投资策略、基于欧式看跌期权及两资产交换期权的套期保值策略．

关键词: 最小收益约束, 最优投资策略, 等价鞅测度

Abstract:

Based on the B lack-Scholes op tion p ricing theory, the equivalent martingale measure is constructed to obtain the op timal strategy of an op timal investment problem. This problem is under the constraint that the return is not less than the maximum of the market return ( random return) and the constant guaranteed return. Meanwhile, by the analysis of the characteristics of this investment problem with HARA utility function, it is concluded that this investment strategy can be simp lified as an unconstrained op timal investment strategy and a hedge strategy based on the European put-op tion and the two-asset exchange option.

Key words: minimum return constraint, optimal investment strategy, equivalent maningale measure

何春雄罗军涂钰青焦健. 最小收益约束下的最优投资问题[J]. 华南理工大学学报（自然科学版）, 2005, 33(3): 95-98,102.

He Chun-xiong Luo Jun Tu Yu-qing Jiao Jian. Optimal Investment Problem Under M inimum Return C0Ilstraint[J]. Journal of South China University of Technology (Natural Science Edition), 2005, 33(3): 95-98,102.