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

ZHU Huainian; CHEN Zhuoyang; BIN Ning

doi:10.13471/j.cnki.acta.snus.2022A062

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

Research articles | 更新时间：2024-09-29

- Robust non-zero-sum stochastic differential portfolio games with two interacting agents under the Heston model
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 63, Issue 4, Pages: 158-169(2024)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2022A062
  CLC： F830.59
- Published：25 July 2024，
  
  Published Online：04 June 2024，
  
  Received：30 August 2022，
  
  Accepted：30 November 2023
- 稿件说明：
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朱怀念,陈卓扬,宾宁.Heston模型下的两人鲁棒非零和随机微分投资组合博弈[J].中山大学学报(自然科学版)(中英文),2024,63(04):158-169.

ZHU Huainian,CHEN Zhuoyang,BIN Ning.Robust non-zero-sum stochastic differential portfolio games with two interacting agents under the Heston model[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(04):158-169.
朱怀念,陈卓扬,宾宁.Heston模型下的两人鲁棒非零和随机微分投资组合博弈[J].中山大学学报(自然科学版)(中英文),2024,63(04):158-169. DOI： 10.13471/j.cnki.acta.snus.2022A062.

ZHU Huainian,CHEN Zhuoyang,BIN Ning.Robust non-zero-sum stochastic differential portfolio games with two interacting agents under the Heston model[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(04):158-169. DOI： 10.13471/j.cnki.acta.snus.2022A062.

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.

Abstract

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

Keywords

portfolio gameNash equilibriumCRRA utilityrelative performancemodel uncertainty

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