Optimal Control Model of Pension Funds Under Continuous Time

In this paper, we consider an retirement, investment and consumption problem based on the basic pension policy of China in continuous time, where the utility function of insured per-son is formulated as an additive of consumption and terminal wealth. In our model, the problem is represented as an optimal stochastic control problem of forward-backward stochastic differential equation(FBSDE). We establish the associated Hamilton-Jacobi-Bellman (HJB) equation via dynamic programming principle. The HJB equation is a fully nonlinear partial differential equation, and we obtain it's numerical solution of the value function as well as the optimal strategies by means of finite difference method. Finally, we analyze the effects of market parameters on the optimal investment, consumption and reinsurance strategies and give some economic explanations.