Optimal investment and benefit strategies for a target benefit pension plan where the risky assets are jump diffusion processes

In this paper, we study the optimal management of a target benefit pension plan. The fund manager adjusts the benefit to guarantee the plan stability. The fund can be invested in a riskless asset and several risky assets, where the uncertainty comes from Brownian and Poisson processes. The aim of the manager is to maximize the expected discounted utility of the benefit and the terminal fund wealth. A stochastic control problem is considered and solved by the programming dynamic approach. Optimal benefit and investment strategies are analytically found and analyzed, both in finite and infinite horizons. A numerical illustration shows the effect of some parameters on the optimal strategies and the fund wealth.