Cooperative Portfolio Selection Game Problem For Two Investors

Optimal portfolio selection is one of the most basic research issues in the field of modern financial economics.It is a study of how rational individual or institutional investors can choose the type and number of investment varieties in the capital market under uncertain conditions.In order to optimize the future consumption or wealth of investors,the optimal asset allocation of limited resources or wealth is carried out across periods.Diversified investment can improve the balance between investors’ risks and returns,but it is difficult for a single investor to hold a large number of stocks to ensure a good risk diversification of the investment portfolio.In addition,due to the limitation of each investor’s time,experience,funds,and expertise in investment fields,and holding a decentralized portfolio may trigger higher transaction costs.Therefore,if several investors cooperate,it is possible to achieve decentralization,specialization and lower transaction costs.Therefore,systematically studying the game of cooperative portfolio selection among investors is of great significance both in theory and in investment practice.First,a single-term cooperative investment selection game model between two investors is constructed,and a Nash equilibrium investment strategy is defined.Under the normal distribution of risk stock returns and the exponential utility function of investors,under the goal of utility maximization,the Nash equilibrium investment strategy and the corresponding terminal wealth utility display solutions are obtained.The results show that whether the cooperation between investors will affect their risk taking depends on the correlation between risky stocks.When the returns of risky stocks are negatively correlated or independent of each other,cooperation between investors will increase their risk-taking.When the returns of risky stocks have a strong positive correlation,cooperation between investors will reduce their risk exposure.Whether the cooperation between investors will increase their utility returns depends on the terminal wealth distribution method and the investor’s risk aversion coefficient.If two investors have the same initial relative risk aversion coefficient,after the cooperation,they can obtain utility returns and the deterministic equivalence will increase.Then a multi-period cooperative investment selection game model between two investors is constructed.Under the condition that the terminal wealth utility is expected to be maximized,the equilibrium investment strategy and value function display expressions are obtained.The cooperative investment strategy and Nash equilibrium investment strategy and the influence of the value function has obtained the conditions for both investors to effectively use the returns.The results show that whether the cooperation between investors affects investors’ risk-taking depends on the Sharpe ratio between risk stocks and the correlation between risk stocks.If the returns of risky stocks are independent of each other,when the ratio of the initial relative risk aversion coefficient of the two investors is between(1/2,2),both investors can obtain utility returns,and the cooperation is solid.of.When the returns of risky stocks are negatively correlated,the area where both parties effectively use returns becomes wider,and cooperation is easier to achieve;when the returns of risky stocks are positively correlated,the areas where both parties effectively use returns are narrowed and cooperation more difficult to achieve.