Optimal Investment Strategy for DC Pension Plan with Default Risk under Jump-Diffusion Model

This paper investigates the optimal investment problem of DC pension personal accounts under jump diffusion model. Suppose a pension manager invests in a risk-free asset, a stock and a defaultable bond, where the wage process and the stock price process obey the jump-diffusion model. Since wage replacement rate is an important standard to evaluate pension management performance, this paper establishes an optimal control model with actuarial present value of wage replacement rate as the optimization goal. An explicit expression for optimal investment strategy and value function is obtained by solving the corresponding Hamilton-Jacobi-Bellman equation using dynamic programming method. Finally, the numerical analysis shows that the jump in the process of stock price and the insured's salary have a significant impact on the optimal investment strategy. When the salary of the insured is likely to rise, the managers will increase the investment in stocks and defaultable bonds. When stock prices are likely to rise, the managers will increase their investment in stocks.