Optimal Investment-Consumption and Life Insurance Strategy with Mispricing and Model Ambiguity

In this paper, we consider the optimal investment-consumption and life insurance strategy for a wage earner who has uncertain labor income described by an Ornstein-Uhlenbeck process. In addition to consumption and purchasing life insurance, the wage earner invests his wealth in the financial market, which consists of a risk-free asset, a market index, and a pair of risky assets with mispricing. Our aim is to maximize the expected utilities obtained from consumption, bequest, or his wealth at the end of the decision horizon. With the dynamic programming approach, we obtain explicit solutions for the optimization problem by solving the corresponding HJB equation. Finally, several numerical examples are presented to illustrate our results.