基于厚尾分布的非寿险准备金评估模型

未决赔款准备金评估是财产保险公司偿付能力管理的核心工作,通常使用的评估方法是广义线性模型.当增量赔款数据存在尖峰厚尾特征时,广义线性模型的传统分布假设可能与实际数据不相符合.此外,保险公司的多条业务线之间往往存在一定的相依关系,这就要求对总准备金的评估结果进行相应调整.本文使用三种新的厚尾分布(即幂Frechet分布、广义对数Moyal分布和全尾伽马分布)代替传统模型中使用的伽马分布、对数正态分布和GB2分布假设,考察它们在未决赔款准备金评估中的应用效果,并应用Copula函数描述了不同业务线之间的相依关系.借助参数化bootsrap和蒙特卡罗随机模拟方法,给出了准备金的预测分布和风险度量值.基于一组实际数据的研究结果表明,厚尾分布对于改善未决赔款准备金的预测效果具有很高的应用价值,而相依性的调整也使得准备金的预测结果更加合理.

Non-life loss reserving models based on heavy-tailed distributions

The estimation of outstanding claims reserve is the core work of solvency management in Property & Casualty insurance companies. Common methods for claims reserving are generalized linear models (GLMs). However, traditional distributional assumptions of GLMs may not match actual incremental losses when the heavy-tailed feature exists, and meanwhile, dependencies among multiple run-off triangles also require a model to combine reserve assessments of individual lines of business (LoBs). This paper replaced traditional assumptions of gamma, lognormal and GB2 distributions with three new heavy-tailed distributions (i.e. exponentiated Fréchet distribution, generalized log-Moyal distribution and full tails Gamma distribution), investigated their application effects in outstanding claims reserving and finally applied Copula regressions to describe dependent structures among different LoBs. The predictive distribution and risk measurements of total reserves can be obtained by parametric bootstrap and Monte Carlo simulations. The empirical results based on an actual dataset show that, heavy-tailed distributions are of high values in improving the prediction of outstanding claims reserves, and the adjustment of reserves' dependencies makes the prediction more rational.