Heston模型下的两人鲁棒非零和随机微分投资组合博弈  

Robust non-zero-sum stochastic differential portfolio games with two interacting agents under the Heston model

作　　者：朱怀念[1] 陈卓扬 宾宁[2] ZHU Huainian;CHEN Zhuoyang;BIN Ning(School of Economics,Guangdong University of Technology,Guangzhou 510520,China;School of Management,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]广东工业大学经济学院,广东广州510520 [2]广东工业大学管理学院,广东广州510520

出　　处：《中山大学学报（自然科学版）（中英文）》2024年第4期158-169,共12页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家社会科学基金(21FJYB025);广东省基础与应用基础研究基金(2023A1515012335);广东工业大学2024年度校级大学生创业训练计划项目(xj2024118451031)。

摘　　要：用Heston模型描述风险资产的价格动态,构建了包含一种无风险资产和一种风险资产的金融市场,投资者可以将其财富自由地配置于无风险资产和风险资产中.考虑到投资者之间经济行为的随机博弈,用相对业绩刻画投资者之间的博弈行为,同时考虑模型的不确定性,以最大化最坏情境下投资者相对业绩的期望效用为目标,构建了包含两个投资者的鲁棒非零和随机微分投资组合博弈模型,利用动态规划方法分别求得了CRRA效用下Nash均衡策略的解析表达,借助数值仿真算例进行了参数的敏感性分析并给出了相应的经济意义阐释.研究发现:相较于不涉及市场竞争的传统投资策略,竞争将使投资者产生羊群效应,跟风投资风险资产,致使金融市场的系统性风险上升.此外,与不考虑模型不确定性相比,模型的不确定性使得投资者减少对风险资产的投资.The stochastic differential portfolio game between two competing investors with undertaking of the relative performance concerns is studied.Assume that the financial market is composed of a risk-free asset and a risky asset whose price process is described by the classical Heston model.Under the framework of Nash equilibrium theory,a non-zero-sum stochastic differential portfolio game model is constructed which maximizes the expected utility of the terminal relative performance.Utilizing the dynamic programming principle,explicit expressions of the value functions and Nash equilibrium for portfolio decisions are obtained under the representative case the CRRA utility.Finally,some numerical examples are performed to illustrate the influence of model parameters on the Nash equilibrium together with some economic interpretations.Results show that,the best response of each investor to the competition is to mimic the strategy of its opponent.Consequently,the portfolio decision of an investor with the relative performance concern is more risky than that without the relative performance concern,and thus increases the systemic risk in financial markets.Moreover,model uncertainty will cause an risk-averse investor to adopt more conservative investment strategies than an ambiguity-neutral investor,which is reflected in the reduction of the amount invested in the risky asset.

关 键 词：投资组合博弈 纳什均衡 CRRA效用 相对业绩 模型不确定性 

分 类 号：F830.59[经济管理—金融学]