方差保费原理下基于普惠型医疗保险的广义承保方式最优策略研究  

The Optimal Strategy of Generalized Underwriting with the Variance Premium Principle for the Inclusive Health Insurance

作　　者：胡少勇[1] 尹薇玥 胡军[1] HU Shaoyong;YIN Weiyue;HU Jun(School of Finance,Jiangxi University of Finance and Economics,Nanchang,330013,China;Department of Insurance,Southwestern University of Finance and Economics,Chengdu,611130,China)

机构地区：[1]江西财经大学金融学院,南昌330013 [2]西南财经大学保险系,成都611130

出　　处：《应用概率统计》2022年第4期617-632,共16页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the MOE(Ministry of Education in China)Project of Humanities and Social Sciences(Grant Nos.20YJA790062,18YJC790050);Jiangxi Province Social Science Planning Project(Grant Nos.19YJ12,18YJ26);Jiangxi Province Education Department Science and Technology Project(Grant Nos.GJJ180245,GJJ170327).

摘　　要：近年来,各类普惠型医疗险项目在全国各大城市纷纷落地,其中以“卫惠保”为代表,采用了同时涵盖比例、免赔额与赔款上限的多层次承保方式,这类承保方式从未作为最优合同形式在已有文献中出现过.本文旨在寻找同时包含比例、免赔额和赔款上限的广义承保方式的最优策略.我们考虑以下两种模型:投保人自留风险的CTE小于风险承受上限情形下且最小化投保人保费的最优保险模型;方差保费原则下最小化保险公司VaR的最优再保险模型.这两种模型得到的最优合同形式支持了“卫惠保”等普惠型医疗险项目的承保方式,文章的最后给出了帕累托分布和伽玛分布下的数值模拟验证.A lot of inclusive health insurance projects have been brewing in many cities in China.Among them,“WeiHuiBao”,which adopts a multi-layer reinsurance method that includes proportion,deductibles,and limit,has attracted our attention.We define such an underwriting method with proportion,deductibles,and limit simultaneously as generalized underwriting method,which has never appeared as the optimal contract in existing literature but very common in reality.This paper aims at finding an optimal strategy in a two-layer generalized underwriting method.We solve two models,the optimal insurance model minimizing the premiums of policy-holders with the CTE of policy-holders’own risk less than an agreed threshold,and the optimal reinsurance model minimizing the VaR of insurer’s total risk,under the variance premium principle,respectively.We find that the optimal contract forms of the two models support the clauses in“WeiHuiBao”,and the numerical solutions under the Pareto distribution and the Gamma distribution are given.The underwriting form of“WeiHuiBao”is a multi-layer generalized underwriting method while this paper demonstrates the optimality of the two-layer underwriting method.

关 键 词：广义承保方式 方差保费 CTE VAR 

分 类 号：O211.9[理学—概率论与数理统计]