Optimal investment-consumption-insurance strategy in a continuous-time self-exciting threshold model

In this paper, we consider an optimal investment-consumption-insurance purchase problem for a wage earner. We assume that the price of the risky asset is governed by a continuous-time, finite state self-exciting threshold model. In this model, the state space of the price of the risky asset is partitioned by a set of thresholds and the parameters depend on the region which the current value of the price falls in. The wage earner’s objective is to find the optimal investment-consumption-insurance strategy that maximizes the expected discounted utilities. The optimal strategy for power utility function is derived by the martingale approach and the dynamic programming approach. Numerical examples are also provided to illustrate the effect of the thresholds.