Robust optimal investment and benefit payment adjustment strategy for target benefit pension plans under default risk

Abstract

In this paper, we consider the optimal investment and benefit payment problem for a target benefit plan (TBP) with default risk and model uncertainty. The pension fund is invested in a risk-free asset, a stock and a defaultable bond. The objective is to maximize the wealth and benefit excess from the target value or minimize the wealth and benefit gap from the target value with exponential function. Applying stochastic control approach, we establish the Hamilton–Jacobi–Bellman equations for both the post-default case and the pre-default case, respectively. Robust optimal investment strategies and benefit payment adjustment strategies are derived explicitly for the two cases. We also consider the non-ambiguity model for degenerate case and compare the results under two scenarios. Numerical analysis is provided to illustrate the effects of parameters on the optimal strategies and demonstrate the properties of the strategies.