Martingale method for optimal investment and proportional reinsurance

Numerous researchers have applied the martingale approach for models driven by Lévy processes to study optimal investment problems. This paper considers an insurer who wants to maximize the expected utility of terminal wealth by selecting optimal investment and proportional reinsurance strategies. The insurer’s risk process is modeled by a Lévy process and the capital can be invested in a security market described by the standard Black-Scholes model. By the martingale approach, the closed-form solutions to the problems of expected utility maximization are derived. Numerical examples are presented to show the impact of model parameters on the optimal strategies.