Optimal investment and benefit payment adjustment strategies for the target benefit plan under partial information

This article investigates the optimal asset allocation and benefit adjustment problem for the target benefit plan (TBP) with predictable returns in an environment of partial information. We assume that the return rate of the stock depends on an observable and an unobservable state variables, and the pension manager estimates the unobservable component from known information through Bayesian learning. Under the criterion of expected exponential utility maximization, we obtain the optimal strategy in closed-form through the dynamic programming principle approach. Furthermore, numerical simulations are conducted by the Monte Carlo method to discuss the impacts of some parameters on the derived optimal strategy and to compare the optimal strategy with the suboptimal strategy when ignoring learning. It turns out that neglecting learning affects the optimal strategy seriously, thereby leading to significant utility losses.