Equilibrium strategies in a defined benefit pension plan game with regime switching

This paper studies the optimal management of an aggregated overfunded pension plan of defined benefit type as a stochastic differential game in a Markovian regime-switching environment. In this asymmetric two-player game, the worker participants act collectively as a single player that claims a share of the surplus, and the sponsoring firm acts as the player who cares about the investment of the surplus fund assets. We formulate the game model in two scenarios, and use the dynamic programming technique to derive the coupled Hamilton-Jacobi-Bellman equations in each scenario. Furthermore, we propose an efficient algorithm that incorporates a kind of quasi-Newton method and the Runge-Kutta scheme to obtain the equilibrium strategies. Finally, we employ a numerical example to verify our algorithm and analyze the impact of model parameters.