Abstract:

This paper considers the optimal investment and optimal contribution-benefit adjustment strategies of a continuous time collective hybrid pension plan with model uncertainty and default risk. We assume that pension funds are invested in a risk-free asset, a defaultable bond and a stock satisfied 4/2 random volatility model. The objective is to maximize the discount value of surplus and contribution-benefit adjustment amount or minimize the discount value when surplus and contribution-benefit adjustment amount are negative based on the CARA utility function. Firstly, applying stochastic optimal control approach, we establish the Hamilton-Jacobi-Bellman equations for both the pre-default case and the post-default case, respectively. Then, we derive the closed-from solutions for robust optimal strategies and corresponding value functions. Finally, numerical analyses illustrate the influence of model parameters and financial market parameters on optimal control problems.

Key words: hybrid pension, 4/2 stochastic volatility model, default risk, model uncertainty