基于copula回归模型的损失预测

在非寿险损失预测的广义线性模型中,通常假设损失次数与损失强度相互独立,事实上二者之间往往存在一定的相依关系,可通过copula函数来刻画.在损失已经发生的条件下,假设损失次数服从零截断泊松分布,损失强度服从伽玛分布,可以建立损失次数与损失强度相互依赖的copula回归模型.把损失强度的分布扩展到逆高斯分布,并将此模型应用于一组车险保单数据进行实证研究.结果表明:该模型不但在损失预测方面优于独立假设下的广义线性模型,而且也优于损失强度服从伽马分布假设下的copula回归模型.

Loss Prediction Using Copula--Based Regression Models

It is generally assumed that loss frequency and loss severity are independent in generalized linear models, but the fact is that they are often dependent. Their dependency may be described by copula functions. Assuming that the loss frequency follows zero--truncated Poisson distribution and the loss severity follows Gamma distribution under the condition that the loss has occurred, the copula--based regression models may be used to predict losses. The paper extends the loss severity distribution from Gamma to inverse Gaussian, and applies the model to a portfolio of car insurance policies, the result shows that the new copula regression model is superior to independent GLM and also superior to copula regression models with Gamma severity distribution assumption.