Equilibrium Reinsurance Strategy and Mean Residual Life Function

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Dan-ping Li, Lv Chen, Lin-yi Qian, Wei Wang
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引用次数: 0

Abstract

In this paper, we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk. Since Mean Residual Life (MRL) has a close relationship with the tail of the distribution, we consider two classes of risk distributions, Decreasing Mean Residual Life (DMRL) and Increasing Mean Residual Life (IMRL) distributions, which can be used to classify light-tailed and heavy-tailed distributions, respectively. We assume that the underlying risk process is modelled by the classical Cramér-Lundberg model process. Under the mean-variance criterion, by solving the extended Hamilton-Jacobi-Bellman equation, we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL, respectively. Furthermore, we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy. We find that under the case of DMRL, if the distribution and the risk aversions satisfy certain conditions, the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy, and under the case of IMRL, the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.

均衡再保险策略和平均剩余寿命函数
本文分析了均衡再保险策略与风险分布尾部之间的关系。由于平均余寿(MRL)与分布尾部关系密切,我们考虑了两类风险分布,即递减平均余寿分布(DMRL)和递增平均余寿分布(IMRL),它们可分别用于划分轻尾分布和重尾分布。我们假设基本风险过程是由经典的 Cramér-Lundberg 模型过程模拟的。在均值-方差准则下,通过求解扩展的汉密尔顿-雅各比-贝尔曼方程,我们分别得出了 DMRL 和 IMRL 下保险人和再保险人的均衡再保险策略。此外,我们还分析了如何选择再保险费才能使保险人和再保险人达成相同的再保险策略。我们发现,在 DMRL 的情况下,如果分布和风险厌恶满足一定条件,保险人和再保险人可以采用一种再保险费率来达成再保险策略,而在 IMRL 的情况下,保险人和再保险人只能相互同意保险人不购买再保险。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
70
审稿时长
3.0 months
期刊介绍: Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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