随机利率环境下一类跳扩散相依风险资产的最优投资策略

doi:10.15960/j.cnki.issn.1007-6093.2020.03.008

运筹学学报 ›› 2020, Vol. 24 ›› Issue (3): 101-114.doi: 10.15960/j.cnki.issn.1007-6093.2020.03.008

随机利率环境下一类跳扩散相依风险资产的最优投资策略

孙景云^*, 郭精军

兰州财经大学统计学院, 兰州 730020

收稿日期:2019-01-02 发布日期:2020-09-05
通讯作者: 孙景云 E-mail:sunjy@lzufe.edu.cn
基金资助:
国家自然科学基金（Nos.71701084，71961013），甘肃省高等学校创新能力提升项目（No.2019A-060），甘肃省科技厅软科学项目（No.1604ZCRA024）

Optimal investment strategies for a class of risky assets with jump-diffusion dependence under the stochastic interest rate

SUN Jingyun^*, GUO Jingjun

School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, China

Received:2019-01-02 Published:2020-09-05

摘要/Abstract

摘要： 考虑了随机利率环境下基于连续时间的动态最优资产配置问题。假设市场利率满足一个均值回复的随机过程，且金融市场由一个零息债券和两个价格受到共同冲击的相依性风险资产所构成。在均值-方差目标准则之下，利用随机最优控制理论和Lagrange对偶原理获得了有效投资策略以及相应有效边界的解析式。最后通过数值算例，分析了有效策略及有效边界对相关参数的敏感性，并验证了相关理论结果。

关键词: 随机利率, 跳扩散相依, 均值-方差准则, Hamilton-Jacobi-Bellman方程, 有效边界

Abstract: In this paper, we consider the continuous time dynamic optimal asset allocation problem under the stochastic interest rate. We suppose that the market interest rate satisfies a stochastic process with the characteristic of mean-reverting, and the financial market consists of a zero-coupon bond and two dependent risky assets whose prices are suffered a common shock. Under the mean-variance criterion, using stochastic optimal control theory and Lagrange dual principle, the analytical solution for the efficient investment strategies and corresponding efficient frontier are obtained. Finally, through numerical examples, the sensitivity of efficient strategies and efficient frontier to relevant parameters are analyzed, and the relevant theoretical results are also verified.

Key words: stochastic interest rate, jump-diffusion dependence, mean-variance criteria, Hamilton-Jacobi-Bellman equation, efficient frontier

中图分类号:

F830.59
F224

孙景云, 郭精军. 随机利率环境下一类跳扩散相依风险资产的最优投资策略[J]. 运筹学学报, 2020, 24(3): 101-114.

SUN Jingyun, GUO Jingjun. Optimal investment strategies for a class of risky assets with jump-diffusion dependence under the stochastic interest rate[J]. Operations Research Transactions, 2020, 24(3): 101-114.

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随机利率环境下一类跳扩散相依风险资产的最优投资策略

Optimal investment strategies for a class of risky assets with jump-diffusion dependence under the stochastic interest rate

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