Management Strategies for the Defined Benefit Pension Fund Under Stochastic Framework

Abstract In this article, we analyze the optimal contributions and investment strategies problem for a defined benefit pension fund. The pension fund manager allocates the capital in riskless and risky assets and the dynamics of the risky asset price follows the Hull and White stochastic volatility model. The choice of the Hull and White model is due to its mean-reverting property. The stochastic dynamic programing principle is used to derive the Hamilton-Jacob-Bellman (HJB) equation. Due to the complications of the HJB when finding the closed form solution, we use the Legendre transform and dual theory to transform the primary problem into a dual one. Furthermore, we obtain the closed form solutions for optimal strategies for the logarithm utility functions by variable transformation technique. Finally, a numerical example is conducted to analyze the effects of parameters in the model and provide some economic implications. To conclude, the Hull and White stochastic volatility model shown to have a substantial impact on the optimal investment strategies and thus can be exploited appropriately to improve the final wealth of the pension fund.