地震指数保险的帕累托最优赔付比例研究——以EQⅡ产品为例
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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。
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.
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.
引文
[1] 范红梅.云南房屋地震保险经营模式研究[J].上海保险,2016,(2):45.
[2] 高孟潭.基于泊松分布的地震烈度发生概率模型[J].中国地震,1996,12(2):195.
[3] 田玲,孙宁,杨琛.基于CARA效用的帕累托最优地震指数保险设计[J].保险研究,2018,(2):17.
[4] 卓志,段胜.构建中国特色巨灾指数:思路与条件[J].财经科学,2013,(1):28.
[5] Babcock B A,Choi E K,Feinerman E.Risk and Probability Premiums for CARA Utility Functions[J].Journal of Agricultural and Resource Economics,1993,18(1):17.
[6] Borch K H.Some Elements of a Theory of Reinsurance.Journal of Risk and Insurance[J].1961,28(3),35-43.
[7] Fan J,Truong Y K.Nonparametric Regression with Errors in Variables[J].The Annals of Statistics,1993,21(4):1900.
[8] Goes A,Skees J R.Financing Natural Disaster Risk Using Charity Contributions and Ex Ante Index Insurance[R].2003.
[9] Golubin A Y.Pareto-Optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value[J].The Journal of Risk and Insurance,2006,73(3):469.
[10] International Finance Corporate.Earthquake Index Insurance Brochure[R/OL].(2018-06-01)[2018-07-01].https://www.ifc.org/wps/wcm/connect/industry_ext_content/ifc_external_corporate_site/industries/financial+markets/retail+finance/insurance/earthquake+index+insurance%2C+indonesia.
[11] Jiang W,Ren J,Yang C,Hong H.On Optimal Reinsurance Treaties in Cooperative Game under Heterogeneous Beliefs[J].Insurance:Mathematics and Economics.2019,85:173.
[12] Raviv A.The Design of an Optimal Insurance Policy[J].The American Economic Review,1979,69(1):84.
[13] Schlesinger H.The Decomposing Catastrophic Risk[J].Insurance:Mathematics and Economics,1999,24(1-2):95.
[14] Shao J,Pantelous A,Papaioannou A D.Catastrophe Risk Bonds with Applications to Earthquakes[J].European Actuarial Journal,2015,5(1):113.
[15] Wang X F,Wang B.Deconvolution Estimation in Measurement Error Models:The R Package decon[J].Journal of Statistical Software,2011,39(10):1.
[16] Zimbidis A A,Frangos N E,Pantelous A A.Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds[J].ASTIN Bulletin,2007,37(1):163.
(1)CARA效用或称指数效用通常被用于研究风险决策问题(Babcock et al.,1993)。
[2] 高孟潭.基于泊松分布的地震烈度发生概率模型[J].中国地震,1996,12(2):195.
[3] 田玲,孙宁,杨琛.基于CARA效用的帕累托最优地震指数保险设计[J].保险研究,2018,(2):17.
[4] 卓志,段胜.构建中国特色巨灾指数:思路与条件[J].财经科学,2013,(1):28.
[5] Babcock B A,Choi E K,Feinerman E.Risk and Probability Premiums for CARA Utility Functions[J].Journal of Agricultural and Resource Economics,1993,18(1):17.
[6] Borch K H.Some Elements of a Theory of Reinsurance.Journal of Risk and Insurance[J].1961,28(3),35-43.
[7] Fan J,Truong Y K.Nonparametric Regression with Errors in Variables[J].The Annals of Statistics,1993,21(4):1900.
[8] Goes A,Skees J R.Financing Natural Disaster Risk Using Charity Contributions and Ex Ante Index Insurance[R].2003.
[9] Golubin A Y.Pareto-Optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value[J].The Journal of Risk and Insurance,2006,73(3):469.
[10] International Finance Corporate.Earthquake Index Insurance Brochure[R/OL].(2018-06-01)[2018-07-01].https://www.ifc.org/wps/wcm/connect/industry_ext_content/ifc_external_corporate_site/industries/financial+markets/retail+finance/insurance/earthquake+index+insurance%2C+indonesia.
[11] Jiang W,Ren J,Yang C,Hong H.On Optimal Reinsurance Treaties in Cooperative Game under Heterogeneous Beliefs[J].Insurance:Mathematics and Economics.2019,85:173.
[12] Raviv A.The Design of an Optimal Insurance Policy[J].The American Economic Review,1979,69(1):84.
[13] Schlesinger H.The Decomposing Catastrophic Risk[J].Insurance:Mathematics and Economics,1999,24(1-2):95.
[14] Shao J,Pantelous A,Papaioannou A D.Catastrophe Risk Bonds with Applications to Earthquakes[J].European Actuarial Journal,2015,5(1):113.
[15] Wang X F,Wang B.Deconvolution Estimation in Measurement Error Models:The R Package decon[J].Journal of Statistical Software,2011,39(10):1.
[16] Zimbidis A A,Frangos N E,Pantelous A A.Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds[J].ASTIN Bulletin,2007,37(1):163.
(1)CARA效用或称指数效用通常被用于研究风险决策问题(Babcock et al.,1993)。