مشخصات پژوهش

This paper investigates the optimal risk management strategies in a general compound Poisson risk model consisting of safety loading of insurer and reinsurance to minimize the infinite-time ruin probability. Its price process is perturbed by a geometric Brownian motion with the drift and volatility of risky asset. In addition, we allow this company to buy proportional reinsurance to reduce the underlying risk and invest its surplus in a risky asset whose price is driven by correlated Brownian motions. We focus on the possibility of an insurance company utilizing optimal controls and study the optimization problem of minimizing the infinite-time ruin probability in a financial market. For the diffusion approximation of risk model, we obtain an analytic expression for the minimum infinite-time ruin probability and the corresponding optimal controls by using the martingale approach. Since it is not easy to derive the explicit expression for the infinite-time ruin probability of perturbed risk model, we obtain the optimal strategies to maximize the Lundberg exponent when the claim amounts are identically distributed and have an exponentially decaying tail. Moreover, we study the effect of investment on the ruin probability in both perturbed risk models. Finally, some numerical examples are conducted to illustrate the effects of model parameters on the optimal risk management strategies and on the financial market.