Abstract:

This paper considers the optimal investment and benefit payment problem for target benefit pension plan with default risk and model uncertainty. We assume that pension funds are invested in a risk-free asset, a defaultable bond and a stock satisfied a constant elasticity of variance(CEV) model. The payment of pensions depends on the financial status of the plan, with risk sharing between different generations. At the same time, in order to protect the rights of pension holders who dies before retirement, the return of premiums clauses is added to the model. In addition, our model allows the pension manager to have different levels of ambiguity aversion, instead of only considering extremely ambiguity-averse attitude. Using the stochastic optimal control approach, we establish the Hamilton-Jacobi-Bellman equations for both the post-default case and the pre-default case, respectively. We derive the closed-form solutions for α-robust optimal investment strategies and optimal benefit payment adjustment strategies. Finally, numerical analyses illustrate the influence of financial market parameters on optimal control problems.

Key words: Target benefit plan, α-robust, Intergenerational risk sharing, Default risk, Return of premiums