模型暧昧下基于CRRA效用准则的非零和投资博弈  

Non-Zero-Sum Stochastic Differential Investment Games in Ambiguous Economy Based on CRRA Utility Criterion

作　　者：朱怀念[1] 莫仕茵 ZHU Huainian;MO Shiyin(School of Economics,Guangdong University of Technology,Guangzhou,510520,China;School of Economics&Management,South China Normal University,Guangzhou,510006,China)

机构地区：[1]广东工业大学经济学院,广州510520 [2]华南师范大学经济与管理学院,广州510006

出　　处：《应用概率统计》2025年第1期101-115,共15页Chinese Journal of Applied Probability and Statistics

基　　金：广东省基础与应用基础研究基金项目(批准号:2023A1515012335)资助.

摘　　要：随着社会的不断发展,我们所需要求解模型的复杂度不断上升,模型的不确定性(也称为模型暧昧性,model ambiguity)也在不断扩大.为了更准确地在考虑模型暧昧性下做出投资决策,本文研究了两个具有竞争关系的暧昧厌恶投资者之间的鲁棒非零和投资博弈问题.假设两个投资者均可将财富投资于由一种无风险资产和一种风险资产构成的金融市场中,用相对绩效描述两个投资者之间的竞争关系,构建了鲁棒非零和随机微分投资博弈模型.利用动态规划原理给出了博弈问题对应的HJB(Hamilton-Jacobi-Bellman)方程,通过求解HJB方程得到了均衡投资策略与相应值函数的解析表达.研究发现:(1)与不考虑模型暧昧性情形相比,考虑模型暧昧性能够显著增加投资者的效用水平;(2)激烈的市场竞争环境会使投资者之间产生羊群效应,相互模仿对手的投资决策,采取风险冒进的投资策略,从而增加金融市场的系统风险;(3)相比于传统(即不考虑博弈)的投资策略,当考虑竞争对手的相对绩效时,Nash均衡策略下的投资者更愿意冒高风险去追求高收益,进而拉大自身与对手之间的财富差距,并且投资者的反应敏感系数(也可反映市场竞争的激烈程度)越大,其对风险的偏好程度也越高.With the development of society,the complexity of the model which needs to be solved is increasing,and the uncertainty of the model(also known as model ambiguity)is also expanding.In order to make the investment decisions more accurately with considering the model ambiguity,this paper studies the robust non-zero sum investment game between two competing ambiguity averse investors.Suppose that two investors can invest their wealth in a financial market composed of one risk-free asset and one risky asset,and use the relative performance to describe the competitive relationship between these two investors.A robust non-zero sum stochastic differential investment game model is constructed,and the HJB equation(Hamilton-Jacobi-Bellman equation)corresponding to the game problem is given by using the dynamic programming principle.The analytical expression of the equilibrium investment strategy and the corresponding value function are obtained by solving the HJB equation.The results show that:(1)considering model ambiguity can significantly increase the investor’s utility compared with when model ambiguity is not considered;(2)The fierce market competition environment will cause herding among investors,imitate each other’s investment decisions,and adopt risky investment strategies,thus increasing the systematic risk of the financial market;(3)compared with the traditional investment strategy(without considering the game),when considering the relative performance,investors under the Nash equilibrium strategy are more willing to take high risks to pursue high returns,thus widening the wealth gap between himself and his competitor;and the greater the sensitivity coefficient of investor’s reaction(which can also reflect the intensity of market competition),the higher risk he prefer to take.

关 键 词：非零和投资博弈 暧昧 NASH均衡 HJB方程 

分 类 号：F830.59[经济管理—金融学]