Equilibrium strategies in a defined benefit pension plan game

Abstract

We study the optimal management of an aggregated overfunded pension plan of defined benefit type as a two-player noncooperative differential game. The model’s key fact is to consider the fund surplus as a strategic variable that makes the pension plan more attractive both for current and future participants. We let the worker participants to act collectively as a single player that claims a share of the surplus, and let the sponsoring firm act as the player that cares about the investment of the surplus fund assets. The union’s objective is to maximize the expected discounted utility of the extra benefits claimed. We solve this asymmetric game under two different assumptions on the preferences of the firm: in the first scenario, the firm aims to maximize expected discounted utility derived from fund surplus; while in the second scenario, the firm cares about minimizing the probability that the fund surplus reaches very low values.