Minimizing the benefit risk in a target benefit stochastic pension plan

Abstract

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 rissless asset and a risky asset where the uncertainty comes from Brownian motion process. The manager minimizes the quadratic deviations between benefit and terminal fund with respect to their target values. A weighting factor included in the model indicates the importance of minimizing the deviation of the terminal fund. 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 horizon. An interesting particular case that receives special attention is when the contribution and the targets have an exponential form.