Asset allocation for a DC pension fund under regime switching environment

We consider the portfolio selection problem of a member of a defined contribution pension plan in a hidden Markov-modulated economy modulated by a continuous-time, finite-state, hidden Markov chain whose states represent different hidden states of the underlying economy. The evolution of the chain over time is not observable by the member. We consider the situation that the member aims to maximize the expected utility from terminal wealth. This utility maximization problem of the member is a stochastic optimal control problem with partial observations. We adopt the innovations approach in filtering theory to transform the problem into one with complete observations. We develop a robust filter for the hidden state of the economy and present a robust-filter-based EM algorithm for estimating the unknown parameters.