Bin Zou
University of Connecticut
Title
Optimal Investment, Consumption, and Insurance Strategies Under Claim Habit
Abstract
We study optimal investment, consumption, and deductible insurance problems under claim-history-dependent premium principles in finite horizon. The agent faces compound-Poisson losses and purchases deductible insurance at discrete times (t = 0,1,..,T-1); in the meantime, she invests in a Black–Scholes market and consumes over all t in [0,T]. We introduce a claim habit process that jumps upward when a claim occurs and decays exponentially between two claims, and to capture experience rating, we consider a premium rule that is an increasing function of the agent’s claim habit. This setup leads to an interesting, mixed continuous-discrete stochastic control problem. For general utility functions, we develop a recursive dynamic-programming approach. In the exponential utility case, we obtain the value functions and optimal strategies in (semi)closed form, showing how claim history affects portfolio, consumption, and insurance decisions.