索赔频率与索赔强度的相依性模型

Dependence Models of Claim Frequency and Claim Severity

为了解决索赔频率与索赔强度之间的相依性问题,本文提出了一种相依性调整模型,即首先在索赔频率和索赔强度相互独立的假设下预测纯保费,然后通过索赔频率与索赔强度之间的相关关系对独立性假设下的纯保费预测值进行调整。与现有模型相比,该模型的优点是可以将纯保费的预测值分解为两部分,即独立性假设下的纯保费和相依性对纯保费的影响,便于模型的解释和应用。本文将该方法应用于一组实际数据,并与其他方法进行了比较。实证研究结果表明,本文对纯保费的预测结果在一定程度上优于现有模型,而且更加清晰地揭示了索赔频率与索赔强度之间的相依性对纯保费预测值的影响,即纯保费较低的保单受相依性的影响较大,而纯保费较高的保单受相依性的影响较小。

This article proposes a new method to deal with the dependence of claim frequency and claim severity. First we obtain the pure premium under the independence assumption, and then adjust the pure premium by the correlation coefficient. Compared with the existing models, the advantage of the new method is that the pure premium can be decomposed into two parts, first part is the pure premium under independence assumption, and the second part is the influence of the dependence, which provides an intuitive interpretation of the structure of the pure premium. We apply various models to a set of insurance data and the result shows that the new method is superior to Tweedie models, conditional models, copula models and common random effect models. Moreover, the new method reveals that the dependence has larger influence on the policy with smaller pure premiums