基于三角模糊数的案均赔款模型
|
摘要
针对传统案均赔款法无法度量准备金评估的不确定性问题,提出基于模糊数的案均赔款法。把非对称的三角模糊数引入到案均赔款法之中,得到累计已报案件数和案均赔款的模糊进展因子,进而计算出各个事故年对应的最终赔款的预测区间及相对应的未决赔款;最后通过决策者风险参数和不确定性参数的不同取值,得到准备金的波动性度量。实证证明该方法可以有效度量准备金预测值的不确定性和波动性。
Proposing a payments per claim method based on the fuzzy number, which aims at the problem that the traditional payments per claim method can not measure the uncertainty of reserve assessment. Introducing the asymmetric triangular fuzzy number into payments per claim method to get the fuzzy cumulative number of reported cases and the fuzzy progressive factors of payments per claim. And then calculate the final compensation of the forecast interval and the outstanding claims corresponding the respective accident years. Finally, the volatility measure of the reserve is obtained by the different value of the decision maker's risk parameter and the uncertainty parameter. It is proved that this method can effectively measure the uncertainty and volatility of reserve forecast.
Proposing a payments per claim method based on the fuzzy number, which aims at the problem that the traditional payments per claim method can not measure the uncertainty of reserve assessment. Introducing the asymmetric triangular fuzzy number into payments per claim method to get the fuzzy cumulative number of reported cases and the fuzzy progressive factors of payments per claim. And then calculate the final compensation of the forecast interval and the outstanding claims corresponding the respective accident years. Finally, the volatility measure of the reserve is obtained by the different value of the decision maker's risk parameter and the uncertainty parameter. It is proved that this method can effectively measure the uncertainty and volatility of reserve forecast.
引文
[1] Heberle J,Thomas A.Combining chain-ladder claims reserving with fuzzy numbers[J].Insurance Mathematics & Economics,2014,55(1):96～104.
[2] Bahrami T,Bahrammi M.Claim reserving with fuzzy regression[J].Cumhuriyet Science Journal,2015,36(3):704～709.
[3] Heberle J,Thomas A.The fuzzy Bornhuetter-Ferguson method:An approach with fuzzy numbers[J].Annals of Actuarial Science,2016,10(02):303～321.
[4] Jde Andrés-Sánchez J,Puchades L G V.The valuation of life contingencies:A symmetrical triangular fuzzy approximation[J].Insurance:Mathematics and Economics,2017,72:83～94.
[5] Romaniuk M.Analysis of the insurance portfolio with an embedded catastrophe bond in a case of uncertain parameter of the insurer’s share[C]//Information Systems Architecture and Technology:Proceedings of 37th International Conference on Information Systems Architecture and Technology-ISAT 2016-Part IV.Springer International Publishing,2017:33～43.
[6] 高井贵,赵明清.模糊利率下的寿险精算模型[J].系统工程学报,2010,(5):603～608.
[7] 容炳华.模糊随机利率下的寿险精算模型[D].广州大学,2012.
[8] 苏兴泉.模糊死亡率模型及其整体贴近度的研究[D].厦门大学,2013.
[9] 顾建忠,严广乐.模糊随机环境下的连续型变额生命年金[J].经济数学,2014,31(4):47～51.
[10] 陈静仁,王玉文.模糊数在链梯法索赔准备金中的应用[J].数学的实践与认识,2015,(17):106～112.
[11] 闫春,李延星,孙晓红,刘志博.考虑离群值的非寿险准备金案均赔款法[J].保险研究,2015,(11):15～24.
[12] 李学辉.过离散广义线性模型在未决赔款准备金评估中的应用[D].山东财经大学,2015.
[13] Heberle J,Thomas A.Combining chain-ladder claims reserving with fuzzy numbers[J].Insurance Mathematics & Economics,2014,55(1):96～104.
[14] 孟生旺,刘乐平.非寿险精算学[M].中国人民大学出版社,2007:303～313.
[2] Bahrami T,Bahrammi M.Claim reserving with fuzzy regression[J].Cumhuriyet Science Journal,2015,36(3):704～709.
[3] Heberle J,Thomas A.The fuzzy Bornhuetter-Ferguson method:An approach with fuzzy numbers[J].Annals of Actuarial Science,2016,10(02):303～321.
[4] Jde Andrés-Sánchez J,Puchades L G V.The valuation of life contingencies:A symmetrical triangular fuzzy approximation[J].Insurance:Mathematics and Economics,2017,72:83～94.
[5] Romaniuk M.Analysis of the insurance portfolio with an embedded catastrophe bond in a case of uncertain parameter of the insurer’s share[C]//Information Systems Architecture and Technology:Proceedings of 37th International Conference on Information Systems Architecture and Technology-ISAT 2016-Part IV.Springer International Publishing,2017:33～43.
[6] 高井贵,赵明清.模糊利率下的寿险精算模型[J].系统工程学报,2010,(5):603～608.
[7] 容炳华.模糊随机利率下的寿险精算模型[D].广州大学,2012.
[8] 苏兴泉.模糊死亡率模型及其整体贴近度的研究[D].厦门大学,2013.
[9] 顾建忠,严广乐.模糊随机环境下的连续型变额生命年金[J].经济数学,2014,31(4):47～51.
[10] 陈静仁,王玉文.模糊数在链梯法索赔准备金中的应用[J].数学的实践与认识,2015,(17):106～112.
[11] 闫春,李延星,孙晓红,刘志博.考虑离群值的非寿险准备金案均赔款法[J].保险研究,2015,(11):15～24.
[12] 李学辉.过离散广义线性模型在未决赔款准备金评估中的应用[D].山东财经大学,2015.
[13] Heberle J,Thomas A.Combining chain-ladder claims reserving with fuzzy numbers[J].Insurance Mathematics & Economics,2014,55(1):96～104.
[14] 孟生旺,刘乐平.非寿险精算学[M].中国人民大学出版社,2007:303～313.