经济数学
經濟數學
경제수학
MATHEMATICS IN ECONOMICS
2014年
4期
68-74
,共7页
非寿险%准备金%相依风险%藤Copula%GAMLSS 模型
非壽險%準備金%相依風險%籐Copula%GAMLSS 模型
비수험%준비금%상의풍험%등Copula%GAMLSS 모형
non-life insurance%reserve%dependent risks%Vine Copula%GAMLSS
在假设各个业务线的增量已决赔款服从伽玛分布、逆高斯分布和对数正态分布的基础上，建立了各个业务线增量已决赔款的 GAMLSS 模型，并将此模型应用于一组具有明显异方差的车险数据，拟合效果优于均值回归模型。另外，在多个业务线的准备金估计中，不同业务线之间的相依性通过藤 Copu-la 函数来描述。用 D 藤 Copula 描述相依关系的 GAMLSS 模型对准备金的评估结果既优于独立假设下的GAMLSS 模型和链梯法对准备金的评估结果，同时还刻画了不同业务线之间的尾部相依性。
在假設各箇業務線的增量已決賠款服從伽瑪分佈、逆高斯分佈和對數正態分佈的基礎上，建立瞭各箇業務線增量已決賠款的 GAMLSS 模型，併將此模型應用于一組具有明顯異方差的車險數據，擬閤效果優于均值迴歸模型。另外，在多箇業務線的準備金估計中，不同業務線之間的相依性通過籐 Copu-la 函數來描述。用 D 籐 Copula 描述相依關繫的 GAMLSS 模型對準備金的評估結果既優于獨立假設下的GAMLSS 模型和鏈梯法對準備金的評估結果，同時還刻畫瞭不同業務線之間的尾部相依性。
재가설각개업무선적증량이결배관복종가마분포、역고사분포화대수정태분포적기출상，건립료각개업무선증량이결배관적 GAMLSS 모형，병장차모형응용우일조구유명현이방차적차험수거，의합효과우우균치회귀모형。령외，재다개업무선적준비금고계중，불동업무선지간적상의성통과등 Copu-la 함수래묘술。용 D 등 Copula 묘술상의관계적 GAMLSS 모형대준비금적평고결과기우우독립가설하적GAMLSS 모형화련제법대준비금적평고결과，동시환각화료불동업무선지간적미부상의성。
Under the assumption that the incremental paid claims of every line of business follow gamma distribution, inverse-Gaussian distribution and log-normal distribution,respectively,the corresponding GAMLSS models were established. The models were applied to a heteroscedastic data set of auto insurance claims,and the result shows that GAMLSS models are superior to mean regression models in predicting outstanding claim reserve.In practice,different lines of insurance business are,to some extent and their dependence can be captured by Vine Copula functions.The corresponding Vine Copula and GAMLSS models were established.The result shows that D Vine Copula-based GAMLSS model is superior to independent GAMLSS models and Chain Ladder method in claims reserving,and it also describes the tail dependence of different lines of business.
