Optimal investment and consumption strategies with state-dependent utility functions and uncertain time-horizon

This paper considers the multi-period optimal strategies for an investment-only problem and an investment-consumption problem. The financial market is regime-switching and consists of one risk-free asset and multiple risky assets. The state process of the financial market is modeled by a finite-state Markov chain. Asset returns and utility functions are affected by the states of the financial market. The investment time-horizon is uncertain and exogenous. By adopting the dynamic programming approach, explicit expressions for optimal value functions and optimal investment and consumption strategies are derived. Moreover, some discussions and numerical examples are provided to illustrate our results, which extend some results in the existing literature to more general situations and show some interesting phenomena.