考虑相对收益的最优投资组合选择问题  

Optimal Portfolio Selection Problem under Relative Return Concerns

作　　者：林祥[1] 钱艺平 舒颖斌 LIN Xiang;QIAN Yiping;SHU Yingbin(School of Finance,Zhejiang Gongshang University,Hangzhou,310018,China)

机构地区：[1]浙江工商大学金融学院,杭州310018

出　　处：《应用概率统计》2021年第6期611-626,共16页Chinese Journal of Applied Probability and Statistics

基　　金：浙江省自然科学基金项目(批准号:LY17A010005);教育部人文社科基金项目(批准号:18YJA790051、19YJE790001);浙江工商大学泰隆金融学院科研项目(批准号:TFS20KY009);浙江省软科学研究计划项目(批准号:2019C 35064)资助.

摘　　要：本文研究了连续时间考虑相对收益的风险厌恶投资者的最优投资组合选择问题.假设投资者可以投资于无风险资产和风险股票,并且选择某一与风险股票相关的随机基准作为目标.投资者选择最优的投资组合策略使得终端期望绝对收益和相对收益的权重和效用最大.首先,利用动态规划原理得到最优投资策略和值函数满足的Hamilton-Jacobi-Bellman方程.其次,在投资者具有指数效用函数下,通过求解HJB方程得到了最优投资策略和值函数的显示表达式.然后,分析了相对收益对投资者最优投资策略的影响,结果发现相对收益会改变投资者的风险承担.最后,通过数值计算给出了最优投资策略和值函数与模型主要参数之间的关系.In this paper we investigate a continuous-time optimal portfolio selection problem for a risk-averse investor based on a relative log-return.Investor can invest her wealth in a risk-free asset and a risky stock.The objective of the investor is to exceed the performance of a stochastic benchmark that is not perfectly correlated with the risky stock.Investor chooses a dynamic portfolio strategy in order to maximize her expected terminal utility of the weight sum of absolute log-return and relative log-return.By using the dynamic programming principle,the corresponding Hamilton-Jacobi-Bellman equation of the optimal portfolio strategy and the value function is established.Furthermore,closed-form expressions of the optimal portfolio strategy and the value function under the investor with a exponential utility function are derived.The effect of the relative return on the optimal portfolio strategy is also analyzed.The result shows that the relative return works against a investor's intrinsic risk-taking tendency.Finally,numerical examples are provided to illustrate how the optimal portfolio strategy and the value function change when some model parameters vary.

关 键 词：最优投资选择 随机基准 绝对收益 相对收益 HAMILTON-JACOBI-BELLMAN方程 

分 类 号：O211.9[理学—概率论与数理统计]