Stochastic Differential Game Of Defined Benefit Pension Plan With Community Pension Model

In the age background of population aging,pension has become an inescapable reality for people,so community pension gradually into the public eye has become a hot topic.In the traditional pension model,more attention is paid to a reasonable investment portfolio to ensure the healthy operation of the pension,and there is a lack of measures to deal with the actual aging social group pension structure and operation.Therefore,this paper considers the differential game of a defined-benefit pension plan under the community pension model.The company controls the investment share,and the employees require more community pension funds.This paper studies the evolution of pension pools when individual benefits are a deterministic function and in more general uncertain situations.To solve the above problems,the stochastic differential game model of fixed income pension under different community pension models is established,and the dynamic programming principle HJBI equation is used to obtain the optimal fund investment ratio,the Markov Perfect Nash Equilibrium solution of the proportion of investment in community pension,and the corresponding optimal portfolio and fund evolution equation.The sensitivity analysis of the equilibrium solution is carried out,and the numerical example analysis is carried out according to the real data,which shows the influence of different risk aversion coefficient,discount factor and other parameters on the equilibrium ratio,and reasonable analysis of the realistic factors that may lead to volatility.The results show that when the utility function of CRRA is taken as the objective function,the Markov perfect Nash equilibrium solution is a pair of constants,and the increase of risk aversion,risk-free interest rate and risk fluctuation will reduce the proportion.But in the case of feedback solution,Markov perfect Nash equilibrium solution is a parametric equation that changes with the fund pool.The increase of the evolution process of the fund pool will increase the two,and the return rate and volatility of risky assets will have different effects on the ratio.