Optimal investment strategy for DC pension schemes under partial information

We consider a defined-contribution (DC)-pension-fund-management problem under partial information. The fund manager is allowed to invest the wealth from the fund account into a financial market consisting of a risk-free account, a stock and a rolling bond. The aim of the fund manager is to maximize the expected utility of the terminal wealth. In contrast to the traditional literature, we assume that the fund manager can only observe the stock-price process and the interest-rate process, but the expected return rate of the stock is unobservable, following a mean-reverting stochastic process. We apply a martingale approach and Clark's formula to solve this problem and the closedform representations for the optimal terminal wealth and trading strategy are derived. We further present the results for the constant relative risk aversion (CRRA) function as a special case.