对数收益下机构投资者之间的最优投资选择博弈  

Optimal Investment Selection Game Problems forInstitutional Investors under Log Returns

作　　者：林祥[1] 钱艺平 李成才 LIN Xiang;QIAN Yiping;LI Chengcai(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》2023年第5期682-700,共19页Chinese Journal of Applied Probability and Statistics

基　　金：浙江省哲学社会科学规划课题(批准号:20NDJC108YB);浙江省基础公益项目(批准号:LGN22G030-001);浙江工商大学泰隆金融学院科研项目(批准号:TFS20KY005)资助。

摘　　要：本文研究了连续时间考虑相对收益的两个风险厌恶机构投资者之间的最优投资选择博弈问题.假设机构投资者可以投资于相同的无风险资产和不同的具有相关关系的风险股票,以反映投资的资产专门化.机构投资者选择动态投资策略使得期望终端绝对收益和相对收益权重和的效用最大.首先,我们定义了Nash均衡投资策略.其次,在机构投资者具有指数效用函数下,得到了Nash均衡投资策略和值函数的显示表达式,分析了相对收益对Nash均衡投资策略和值函数的影响,并通过数值计算给出了Nash均衡投资策略与模型主要参数之间的关系.最后,采用确定性等价比较了考虑相对收益的最优投资策略与仅仅考虑绝对收益的最优投资策略的投资绩效,结果表明相对收益会影响机构投资者的投资绩效.In this paper we study a continuous-time optimal portfolio selection game problems between two risk-averse institutional investors when each investor takes into account his relative return by compar-ison to her competitor.Both institutional investors can invest freely in the risk-free asset and only one of the two correlated risky stocks is available to each investor,reflecting asset specialization.Each 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.Wefirst characterize explicitly the unique Nash equilibrium portfolio strategies.Secondly,the Nash equilibrium portfolio strategy and the value function of each in-vestor are obtained in closed forms for the case of each investor with an exponential utility function.The effects of the relative return on the Nash equilibrium portfolio strategies and the value function are also analyzed.Numerical examples are also provided to illustrate how the Nash equilibrium portfolio strategies change when some model parameters vary.The investment performance between the Nash equilibrium portfolio strategy and the traditional strategy is also compared by using the certainty equivalent.The results reveal that the relative return can change the investment performance of the institutional investors.

关 键 词：Nash均衡投资策略 相对收益 绝对收益 指数效用函数 确定性等价 

分 类 号：O211.9[理学—概率论与数理统计]