不完全市场下考虑损失厌恶的连续时间投资组合选择

运筹学学报 ›› 2012, Vol. 16 ›› Issue (1): 1-12.

• 运筹学 • 下一篇

不完全市场下考虑损失厌恶的连续时间投资组合选择

米辉^1,2, 张曙光¹

1. 中国科学技术大学统计与金融系, 合肥, 230026 2. 南京师范大学数学科学学院, 南京, 210046

收稿日期:2011-03-07 修回日期:2011-10-09 出版日期:2012-03-15 发布日期:2012-03-15
通讯作者: 米辉 E-mail:mihui@mail.ustc.edu.cn

Continuous-time Portfolio Selection with Loss Aversion in an Incomplete Market

Mi Hui^1,2, ZHANG Shu-Guang¹

1. Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China; 2. 2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, China

Received:2011-03-07 Revised:2011-10-09 Online:2012-03-15 Published:2012-03-15
Contact: Hui MI E-mail:mihui@mail.ustc.edu.cn
Supported by:
This research is supported by the National Basic Research Program of China (973 Program, Grant No. 2007CB814901).

摘要/Abstract

摘要： 在不完全市场条件下研究了一般情形下的损失厌恶投资者的连续时间投资组合选择模型. 面对市场风险, 投资者的偏好由一个S-型的价值函数定义. 通过把不完全市场转换为完全市场, 利用鞅方法和复制技术, 分别获得了投资者的最优期末财富以及最优投资策略. 最后讨论了一个分段幂函数的例子, 在模型系数为确定的常数情形下, 得到了最优解的显示表达式.

关键词: 损失厌恶, , 投资组合选择, , 不完全市场, 鞅

Abstract: In this study we investigate a general continuous-time portfolio selection model with loss aversion in an incomplete market where the number of stocks is strictly less than the dimension of the underlying Brownian motion. The investor's preference facing market risks is defined by a S-shaped value function. By transforming the market into a complete one, we solve the optimal terminal wealth and the optimal wealth-portfolio pair of agents using martingale method and replicating technique. A special example with a two-piece power function and deterministic coefficients is presented to illustrate the general results. Last, the explicit expressions of the optimal solutions are given.

Key words: loss aversion, portfolio selection, incomplete market, martingale

米辉, 张曙光. 不完全市场下考虑损失厌恶的连续时间投资组合选择[J]. 运筹学学报, 2012, 16(1): 1-12.

Mi Hui, ZHANG Shu-Guang. Continuous-time Portfolio Selection with Loss Aversion in an Incomplete Market[J]. Operations Research Transactions, 2012, 16(1): 1-12.

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不完全市场下考虑损失厌恶的连续时间投资组合选择

Continuous-time Portfolio Selection with Loss Aversion in an Incomplete Market

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