基于Hawkes过程损失厌恶型保险公司最优投资-再保险策略
Hawkes-Based Optimal Investment and Reinsurance Strategies for Loss-Averse Insurer
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摘要: 本文研究一类损失厌恶型保险公司的最优投资-再保险问题.考虑到索赔的发生具有集群性,论文采用Hawkes过程来描述索赔次数,建立复合Hawkes风险模型.假设保险公司经营两类保险业务,针对索赔次数过程的不同衰减强度,研究保险公司的再保险策略.基于S型效用函数,本文以期望效用最大为优化目标,运用鞅方法得到最优投资策略和最优再保险策略的显式解.最后通过数值分析,讨论了模型主要参数对最优策略的影响.根据数值例子的结果发现,当索赔发生的集群性越强,保险公司面临的索赔风险越高,决策者会购买更多的再保险以减少自留风险.Abstract: This paper studies an optimal reinsurance and investment problem for a kind of loss-averse Insurer. Considering that claim events are clustered, this paper adopts Hawkes processes to describe the claim numbers and establishes Hawkes risk model. Insurer is assumed to operate two different classes of insurance businesses, the reinsurance strategies are studied according to the different decay intensities of the claim number processes. In this paper, we assume that the insurer’s goal is to maximize the expected S-shaped utility from the terminal wealth. And explicit solutions of optimal investment and proportional reinsurance strategies are given by martingale approach. Finally, the influence of the main parameters of the model on the optimal strategies is discussed by numerical analysis. In addition, when the claim events are clustered, the higher the claim risk faced by insurer. In this situation, the insurer will buy the more expensive reinsurance to reduce his claim risk.