基于追溯保费原理的最优再保险策略  

The Optimal Retrospective Reinsurance with the Minimum Risk-Adjusted Value

作　　者：温利民[1] 韩菲 WEN Limin;HAN Fei(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang,330022,China;Gannan Health Vocational College,Ganzhou,341000,China)

机构地区：[1]江西师范大学数学与统计学院,南昌330022 [2]赣南卫生健康职业学院,赣州341000

出　　处：《应用概率统计》2023年第3期347-362,共16页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金项目(批准号:72263019、71761019)资助.

摘　　要：追溯保费是一种依赖于保单期保险人实际损失的保费厘定计划,是对过去已经发生的损失进行承保的保险方式.本文将追溯保费应用于再保险模型中,当最优准则选为最小化风险调整值而风险资本用TVaR来度量时,得到的最优分保函数形式为停止损失再保险.进而,研究了最优停止损失再保险中最优自留额的求解算法.最后,假设损失服从指数分布、Pareto分布和Gamma分布等情形,利用数值举例的方法研究了税租乘数T和安全负荷系数ρ对最优自留额和最小风险调整值的影响.结果表明,当其他参数一定时, T增大,最优自留额增大而最小风险调整值减小;而其他参数一定时,最优自留额和最小风险调整值都会随着ρ的增大而增大.Retrospective premium is a premium rating plan that relies on the actual loss of the insurer during the policy period.It underwrites losses that have occurred in the past.The retrospective premium has been used in the reinsurance model in this paper.When the optimal criterion is to minimize the risk-adjusted value and the risk capital is measured by TVaR,the optimal ceded function under this model is in the form of stop-loss reinsurance.The minimum risk-adjusted value and the optimal retention have been obtained.Finally,through numerical simulation,we assumed that the loss has the exponential distribution,Pareto distribution and Gamma distribution,and explored the influence of the tax multiplier T and the parameter ρ on the optimal retention and the minimum risk adjusted-value.The results show that when other parameters are constant,as T increases,the optimal retention increases and the minimum risk-adjusted value decreases,and when other parameters are constant,the optimal retention and the minimum risk-adjusted value both increase with the increase of ρ.

关 键 词：追溯保费原理 风险度量 风险调整值 最优再保险 

分 类 号：O211.9[理学—概率论与数理统计]