《保险研究》20190604-《地震指数保险的帕累托最优赔付比例研究——以EQII产品为例》（田玲、孙宁、杨琛）

［摘   要］EQII是一种利用地震指数确定共同保险赔付比例的新型地震指数保险产品。本文基于巨灾经济损失分解的观点,推导出了帕累托最优EQII保单设计的必要条件,并在CARA效用假设以及地震损失中个体差异的影响为伽马分布的条件下,得出了EQII的帕累托最优赔付比例与地震指数之间的具体函数关系。最后利用中国大陆历年地震损失数据,分别对以地震震级和震中烈度作为指数的EQII产品进行帕累托最优赔付比例体系的设计及定价。本文的研究结果表明,当前EQII产品的保单设计符合帕累托最优的必要条件,并且风险管理能力稍弱的机构也可以根据自身风险偏好设计并发售满足帕累托最优条件的EQII产品。此外,EQII产品的帕累托最优赔付比例设计与地震区划中各区域的地震灾害特点和潜在的目标客户数量有关,因此本文建议EQII的赔付比例应根据各区域地震灾害的具体情况分别进行设计。

［关键词］地震指数保险；共同保险；帕累托最优；赔付比例；保险定价

［基金项目］本文受到国家自然科学基金面上项目“基于指数化结构的地震风险管理研究”(项目批准号:71673206)和国家自然科学基金青年科学基金项目“中国巨灾保险基金制度及其隐含的风险分散信息研究”(项目批准号:71603190)的资助。

［作者简介］田玲,武汉大学经济与管理学院保险与精算系主任,教授、博士生导师,研究方向:风险管理与保险经济学,E-mail:ltian@whu.edu.cn；孙宁,武汉大学经济与管理学院博士研究生,研究方向:风险管理与保险经济学；杨琛,武汉大学经济与管理学院保险与精算系助理教授,北美准精算师,研究方向:风险管理与精算。

The Research on the Pareto Optimal Payment Proportion of Earthquake Index-based Insurance-Taking EQII as the Example

TIAN Ling,SUN Ning,YANG Chen

Abstract：EQII is a new type of earthquake index insurance product that is essentially a type of coinsurance with proportional payments which are determined by the earthquake index.Based on the decomposition of catastrophe losses,this article derived the necessary condition for Pareto optimal policy designs of EQII,and obtained the explicit form of the Pareto optimal payment proportion as a function of the earthquake index under CARA utility assumption and gamma-distributed assumption for the impacts of the individual differences.Finally,given the annual earthquake loss data of mainland China,we designed and priced the Pareto optimal EQII products using magnitude and intensity as the indexes respectively.The result of this article verified that the existing EQII product design met with the necessary condition,and insurers with weaker risk management could design and sell their own Pareto optimal EQII according to their risk preference.Moreover,as the Pareto optimal design of EQII depended on properties of earthquakes and the number of potential clients,we suggested that the design of EQII should vary across different areas according to their specific earthquake situations.

Key words：Earthquake Index-based Insurance；coinsurance；Pareto Optimal；payment proportion；insurance pricing