Robust equilibrium strategies in a defined benefit pension plan game

TL;DR

This paper studies robust strategies in a non-zero-sum game involving an overfunded pension plan, considering worst-case market scenarios and deriving explicit solutions through stochastic dynamic programming.

Contribution

It introduces a novel framework for robust non-zero-sum pension plan games with explicit solutions under ambiguity in financial markets.

Findings

Explicit optimal strategies are derived for both the firm and union.

Numerical results illustrate the economic behaviors of the strategies.

The model accounts for worst-case market scenarios and ambiguity.

Abstract

This paper investigates the robust {non-zero-sum} games in an aggregated {overfunded} defined benefit (abbr. DB) pension plan. The sponsoring firm is concerned with the investment performance of the fund surplus while the participants act as a union to claim a share of the fund surplus. The financial market consists of one risk-free asset and $n$ risky assets. The firm and the union both are ambiguous about the financial market and care about the robust strategies under the worst case scenario. {The union's objective is to maximize the expected discounted utility of the additional benefits, the firm's two different objectives are to maximizing the expected discounted utility of the fund surplus and the probability of the fund surplus reaching an upper level before hitting a lower level in the worst case scenario.} We formulate the related two robust non-zero-sum games for the firm and the union. Explicit forms and optimality of the solutions are shown by stochastic dynamic programming method. In the end of this paper, numerical results are illustrated to depict the economic behaviours of the robust equilibrium strategies in these two different games.