带相关风险的保险公司的最优分红和再保险问题

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

本文的研究对象是带两种相关风险业务的保险公司.本文用复合Poisson过程描述这两种风险;应用扩散逼近理论,建立了一个扩散逼近模型.利用动态再保险策略,公司可以降低其破产概率,同时通过给客户分红,公司可以保持竞争力.公司的目标是寻找最优策略和值函数来最大化期望折现分红.因为超额损失再保险策略优于比例再保险策略,所以,本文考虑公司的超额损失再保险及其分红问题.问题分两种情形讨论:分红率有界和分红率无界.在这两种情形下,本文最终得到了值函数和相应最优策略的具体表达式.

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.