索赔准备金评估的贝叶斯非线性分层模型

Bayesian Non-linear Hierarchical Models for Claims Reserving

基于贝叶斯非线性分层模型的一元索赔准备金评估随机性方法,设计了10种合适的模型结构,将非线性分层模型与贝叶斯方法结合起来,应用WinBUGS软件对精算实务中的经典流量三角形数据进行数值分析,并使用MCMC随机模拟方法得到了各种模型结构下最终损失和索赔准备金的完整预测分布及其分布特征。这种方法克服了其他准备金评估模型存在的缺陷,不但可以考虑不同事故年索赔进展的同质性和差异性,而且可以有效度量尾部进展的不确定性。

The paper proposes Bayesian non-linear hierarchical models for univariate stochastic claims reserving in non-life insurance, designs ten suitable model structures through combining non-linear hierarchical models with Bayesian method, so as to provide some numerical analysis for the classic runoff triangle data in the actuarial practice with WinBUGS software, and further obtains the predictive distributions and relevant distribution characteristics of ultimate loss and claims reserves under various model structures using MCMC stochastic simulation method. The proposed method overcomes some inherent defects of the other reserving models. The method can not only consider the homogeneity and heterogeneity of claims developments in different accident years, but also can measure effectively the uncertainty of tail development.