分层广义线性模型在准备金评估中的建模研究

Modeling Study of Hierarchical Generalized Linear Model in the Assessment of the Reserve

考虑到赔付流量三角形数据同一事故年反复观测的纵向特征以及数据结构的层次性,建立了分层广义线性模型.与通常的随机模型相比,分层广义线性模型不但可以选择条件反应变量的分布而且风险参数分布范围也更加广泛.利用h-似然函数估计分层广义线性模型的模型参数,降低了计算量.为使模型具有可比性,评估模型的预测精度,推导了模型预测误差的估计式.为充分利用已知赔付信息,将赔付额和赔付次数两种赔付信息纳入未决赔款准备金评估模型,建立了两阶段分层广义线性模型.在线性预测量中考虑了各种固定效应和随机效应以及模型结构的散布参数,改进了线性预估量结构.研究表明:分层广义线性模型对于数据的各种分布及形式都具有很好的适应性,更加符合保险实务现实的赔付规律.

By considering the longitudinal characteristics of repeated measurements over time of loss for a given accident year in the loss runoff triangles and regarding the loss runoff triangles as hierarchical data, this paper established a hierarchical generalized linear model. Compared with the usual stochastic model, the hierarchical generalized linear model can choose the distribution of conditional response variables and the distribution of risk parameters is more extensive. Using the h-likelihood function to estimate the model parameters of the hierarchical generalized linear model, the calculation amount was reduced. In order to make the model to be comparable, the prediction accuracy of the model was evaluated, and the estimation formula of the model prediction error was derived. In order to make full use of the known payment information, a two-stage hierarchical generalized linear model was established to consider two payment information -the number of compensation and the amount of compensation. The linear prediction considers the distribution parameters of fixed effects, random effects and the distribution parameters of the model structure. The research shows that the hierarchical generalized linear model has good adaptability to all kinds of distribution and form of the data, and it is more consistent with the real payment rule in the insurance practice.