Robust equilibrium strategy for DC pension plan with the return of premiums clauses in a jump-diffusion model

Abstract

This paper studies a robust equilibrium strategy for a mean-variance defined contribution (DC) pension plan with ambiguity aversion and return of premiums clauses in a jump-diffusion model. Ambiguity-averse members worry about model misspecification and aim to find a robust optimal strategy. In most of DC pension plans, the return of premiums clauses is been often set to protect the rights of plan members. A portion of premiums is usually refunded to members who died during the accumulation phase, while the difference between the sizes of the accumulated fund and the returned premiums is evenly divided among the surviving members. Assume that the financial market contains a risk-free asset and a risky asset, and the price process of risky asset is driven by a jump-diffusion model. We establish a mean-variance model with ambiguity aversion. By using the extended Hamilton–Jacobi–Bellman (HJB) equation, the robust time-consistent equilibrium strategy and the corresponding equilibrium value function are derived. In addition, some special cases are provided in detail. Finally, a numerical example illustrates the impact of model parameters on the robust equilibrium strategy and utility losses.