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Optimal proportional reinsurance with common shock dependence
Institution:1. School of Finance, Guangdong University of Foreign Studies, 510006 Guangzhou, PR China;2. College of Business Administration, Hunan University, 410082 Changsha, PR China;3. School of Finance, Shanghai University of Finance and Economics, 200433 Shanghai, PR China
Abstract:In this paper, we consider the optimal proportional reinsurance strategy in a risk model with multiple dependent classes of insurance business, which extends the work of Liang and Yuen (2014) to the case with the reinsurance premium calculated under the expected value principle and to the model with two or more classes of dependent risks. Under the criterion of maximizing the expected exponential utility, closed-form expressions for the optimal strategies and value function are derived not only for the compound Poisson risk model but also for the diffusion approximation risk model. In particular, we find that the optimal reinsurance strategies under the expected value premium principle are very different from those under the variance premium principle in the diffusion risk model. The former depends not only on the safety loading, time and interest rate, but also on the claim size distributions and the counting processes, while the latter depends only on the safety loading, time and interest rate. Finally, numerical examples are presented to show the impact of model parameters on the optimal strategies.
Keywords:Dependent risks  Hamilton–Jacobi–Bellman equation  Compound Poisson process  Brownian motion  Exponential utility  Proportional reinsurance
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