Abstract: The continuous-time optimal investment problem for a defined contribution (DC) pension plan under an incomplete market is considered in this paper. We take into account the inflation risk which is important but neglected in most studies. Different from many usual models, the proposed model maximizes the expected utility of the actual terminal wealth and can cope with multiple risky assets. By reducing the dimension of the underlying Brownian motions to equal to the number of risky assets, we formulate an auxiliary problem under a complete market. Applying the stochastic dynamic programming method, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation, and obtain the explicit solution under the power utility function. Finally, in order to better understand our results, numerical experiments are carried out to illustrate the effects of main parameters on the optimal strategy.

Key words: DC pension plan, inflation risk, market transformation, stochastic dynamic programming, HJB equation