Research On The Competitive Investment Selection Game Problem Between Fund Managers Under The Mean Variance Criterion

Investment portfolios represent an effective tool for diversifying risk and are crucial for investors.The theoretical basis of investment portfolio construction involves allocating assets efficiently in uncertain environments to strike a balance between maximizing returns and minimizing risks.Institutional investors,in particular,are motivated by the desire to attract new clients,manage larger funds,and advance their own careers,all of which drive them to seek higher returns than their competitors.When deciding on investment strategies,institutional investors must consider their competitors’ investment behaviors fully to balance the trade-off between investment returns and risks.The mean-variance criterion,valued for its simplicity and accessibility,is widely utilized in both theoretical research and investment practice.Therefore,studying the optimal investment strategy selection game between institutional investors,which takes into account their relative performance under the mean-variance criterion,and analyzing the impact of competition among institutional investors on risk-taking,is of significant importance for both theory and investment practice.Firstly,under the mean-variance criterion,we consider the discrete-time multi-period investment strategy selection game between two competitive institutional investors with the same investment opportunity set.A competitive investment strategy selection game model between two institutional investors is constructed under the mean-variance criterion,and Nash equilibrium investment strategies are defined.The Nash equilibrium investment strategy and value function of institutional investors are obtained by discrete-time dynamic programming,and the Nash equilibrium investment strategy and efficient frontier of institutional investors are obtained by the Lagrange duality theory.The research results show that the Nash equilibrium investment strategy of institutional investors is linearly related to their current wealth level.The effective investment strategy of institutional investors not only depends on the sensitivity of institutional investors to relative wealth,but also on the sensitivity of their competitors to relative wealth,showing a nonlinear relationship.The effective frontier of institutional investors depends not only on their own initial wealth,but also on their competitors’ initial wealth,as well as various parameters of risk-free interest rates and stock returns.Secondly,this study examines the time-consistent mean-variance investment strategy selection game between two competitive institutional investors under asset specialization.A time-consistent mean-variance investment strategy selection game model is constructed between two institutional investors under asset specialization,and the Nash equilibrium investment strategy is defined.By solving the corresponding extended Bellman equation,the analytical expressions of Nash equilibrium investment strategy and value function for institutional investors are obtained.Using sensitivity analysis,the relationship between Nash equilibrium investment strategy and value function and the main parameters of the model is determined.The Nash equilibrium investment strategy and value function of institutional investors under competition are systematically compared with the optimal investment strategy and value function of institutional investors under normal conditions.The results show that the Nash equilibrium investment strategy and value function of institutional investors not only depend on their own risk aversion coefficient and sensitivity to relative wealth,but also on the risk aversion coefficient and sensitivity to relative wealth of their competitors,as well as the parameters of the risky stock and risk-free rate.Competition can change institutional investors’ attitudes towards risk-taking,and when the correlation between risky stocks is positive,competition can increase institutional investors’ investment in risky stocks.Regardless of whether institutional investors have the same investment opportunity set,their expected wealth under competition is less than their expected wealth under normal conditions.Finally,in the context of institutional investors’ risk-taking behavior,this research examines the effect of competition on risk-taking between two institutional investors.By introducing a measure of competition based on the relative performance of the two investors,a game-theoretic model is constructed to analyze the impact of competition on risk-taking behavior.The analysis shows that competition among institutional investors can lead to a higher level of risk-taking,which may result in higher expected returns but also greater potential losses.Moreover,the impact of competition on risk-taking behavior is found to be nonlinear and depends on the relative wealth positions of the two investors.Overall,this research contributes to a better understanding of the investment behavior of institutional investors,particularly in the context of portfolio selection and risk-taking.The findings suggest that competition plays a crucial role in shaping institutional investors’ investment decisions and that it can have significant implications for their performance and risk-taking behavior.The insights gained from this research can be valuable for institutional investors and financial practitioners in designing effective investment strategies and managing risk.