A defined benefit pension plan game with Brownian and Poisson jumps uncertainty

Ricardo Josa-Fombellida and Paula López-Casado

European Journal of Operational Research, 2023, vol. 310, issue 3, 1294-1311

Abstract: In this paper, we study the optimal management of an aggregated pension fund of defined benefit type by means of a differential game with two players, the firm and the participants. We assume that the fund wealth is greater than the actuarial liability and then the manager builds a pension fund surplus. In order to contemplate sudden changes in the financial market, the surplus can be invested in a portfolio with a bond and several risky assets where the uncertainty comes from Brownian motions and Poisson processes. The aim of the participants is to maximize a utility of the extra benefits. The game is analyzed in three scenarios. In the first, the aim of the firm is to maximize a utility of the fund surplus, in the second, to minimize the probability that the fund surplus reaches a low level, and in the third, to minimize the expected time of reaching a benchmark surplus. An infinite horizon is considered, and the game is solved by means of the dynamic programming approach. The influence of the jumps of the financial market on the Nash equilibrium strategies and the fund surplus is studied by means of a numerical illustration.

Keywords: Finance; Pension funds management; Stochastic differential game; Poisson jumps; Markov perfect Nash equilibria (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:310:y:2023:i:3:p:1294-1311

DOI: 10.1016/j.ejor.2023.04.014

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