Martingale method for optimal investment and proportional reinsurance
Numerous researchers have applied the martingale approach for models driven by
L′evy 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 L′evy 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.
关键词：
martingale method,
proportional reinsurance,
investment,
exponential utility,
quadratic utility
