Research On The Optimal Investment Strategy Selection Game Between Institutional Investors Under Logarithmic Return

In the financial market,as an important method of effective asset allocation,the essence of portfolio is to reasonably allocate all kinds of assets in the uncertain financial market,so as to realize the balance between maximizing the return of portfolio and minimizing the risk of portfolio.On the one hand,investors hope to maximize the absolute return of investment in order to increase their wealth;On the other hand,investors also pay attention to the relative returns relative to other investors.Higher relative returns imply better investment results under the same market conditions.Especially for institutional investors,higher relative return means higher performance ranking and can attract more funds.Therefore,when institutional investors weigh the return and risk of investment and make investment strategies,they should consider the investment behavior of other competitors in the financial market.Investment income is dimensionless,easy to compare,and has nothing to do with the initial wealth of investors,so investment income is a better indicator of investment performance than wealth.Therefore,it is of great significance to study the relative impact of investors’ choice of investment portfolio,no matter how they choose the investment portfolio in the game theory or practice.Under the asset specialization investment strategy,the optimal investment choice of continuous time institutional investors considering absolute return and relative return is studied,and the optimal investment strategy of institutional investors under the maximum weight and utility of expected terminal absolute return and relative return is obtained.Firstly,a competitive investment choice game model considering relative returns between continuous time institutional investors is constructed under asset specialization,and Nash equilibrium portfolio policy is also defined.Then by using the principle of dynamic programming principal,the Hamilton Jacobi Bellman equation satisfied by Nash equilibrium investment strategy and value function is obtained under the general utility functions of the institutional investors.If the institutional investors have the exponential utility functions,we obtain the explicit expressions of Nash equilibrium investment strategy and value function,and the influence of relative return on the Nash equilibrium investment strategy and value function is also analyzed.Finally,the relationships between the Nash equilibrium investment strategy and the main parameters of the model are also given by numerical simulation.The investment performance of the optimal investment strategy considering relative return and only absolute return is compared by deterministic equivalence.The results show that,unlike institutional investors who only consider absolute return,they will not short the risk stock.When the prices of the two risk stocks are negatively correlated,institutional investors may short the risk stock,and competition changes the attitude of institutional investors towards risk-taking.When the risk stock prices are negatively correlated,the deterministic equivalence is an increasing function of the correlation coefficient.When the risk stock prices are positively correlated,the deterministic equivalence decreases with the increase of the correlation coefficient.Under the investment strategy of asset diversification,the optimal investment choice of the institutional investors considering both relative return and absolute return is studied in continuous time.Firstly,a competitive investment choice game model considering relative returns among the institutional investors under asset diversification is established,and Nash equilibrium portfolio policy of the institutional investors is also defined.Then,if the institutional investors have the exponential utility functions,by using the principle of dynamic programming principal,we obtain the HJB equation satisfied by the Nash equilibrium investment strategy and value function.The explicit expressions of Nash equilibrium investment strategy and value function are obtained by solving HJB equation.Finally,the influence of the characteristic parameters of institutional investors and the characteristic parameters of risky assets on the strategy is discussed,and the investment return utility of institutional investors under asset specialization and asset diversification is compared and analyzed through numerical calculation.The results show that the change of model parameters will have an impact on Nash equilibrium investment strategy and value function.Whether institutional investors adopt asset specialization investment strategy or asset diversification investment strategy depends on the relationship between various model parameters.