Funding and investment decisions in a stochastic defined benefit pension plan with regime switching

摘要

In this paper, we consider a continuous-time Markov regime-switching model for a pension plan with a collective defined benefit character. In particular, we focus on optimal funding and asset allocation problem for a fund manager who wants to maximize the expected utility of the difference ratio between the benefit and contribution rates to the total salary until ruin. Using the techniques and methods of stochastic control, we present a system of Hamilton–Jacobi– Bellman equations for this optimization problem and establish a verification theorem. In the special cases of logarithmic and power utility, we solve the problem explicitly and present some numerical examples to illustrate our results.