Optimal dividend and reinsurance problem for an insurance\\ company with dependent risks

Abstract

In this paper, we consider an insurance company which has two dependent lines of business. Each business is modeled by a compound Poisson risk process. Using the diffusion approximation theory, we get an approximated diffusion model. The company applies a dynamic reinsurance policy to reduce the ruin probability and pays dividends to keep competitive. The objective is to find out the value function and the optimal policy which maximizes the expected cumulative discounted dividend. Since the excess-of-loss reinsurance is more profitable than the proportional reinsurance, we discuss the optimal excess-of-loss reinsurance and dividend problem in this approximate diffusion model. The problem is considered in two situations: The dividend rate is bounded and the dividend rate is unbounded. Since the risks are dependent, five cases need to be dealt with when the dividend rate is bounded and two cases need to be investigated when the dividend rate is unbounded. In both situations, explicit expressions for the value function and the corresponding optimal strategies are obtained.