基于分层贝叶斯模型的损失准备金估计

Estimation of loss reserves based on a hierarchical bayesian model

传统的准备金模型主要是通过加总个体数据得到聚合损失三角形数据建立的,然而,这种数据的加总对原始个体数据产生不可避免的信息浪费.虽然这种方法简单,但可导致准备金估计的较大偏差.近年来提出的个体数据准备金模型中大都没有考虑保单合同之间的相依性.本文假设相同事故年的保单产生的索赔具有某种共同效应导致的相依情形,通过建立个体数据准备金的分层贝叶斯模型,利用信度理论的思想,得到每个事故年的准备金估计,从而得到总准备金的估计.进而,讨论了发展因子和结构参数的估计及其相应的统计性质.最后,给出数值例子表明本文给出的准备金估计的计算方法,并且比较了个体数据和聚合数据下准备金估计的均方误差.

Traditional loss reserve models are mainly based on aggregate loss triangles,in which the entries are obtained by summations of individual loss data.The summation procedures inevitably cause wastage of information contained in the raw individual data.Though this method is simple,it results in a larger error in the estimate of loss reserves.Individual loss reserve models emerging in recent years have failed to consider dependencies between policies.This article assumes the existence of certain common random effects between policies in the same accident year.Thus,a hierarchical bayesian model is built for individual data loss reserves.Using the ideas of credibility theory,we get the credibility estimate of loss reserves in each accident year,and thus the total reserve.In addition,the estimation of structural parameters and development factors are discussed.And the statistical properties are derived for those estimators of structural parameters.Finally,a numerical example is given to show the calculations with our estimators,and simulations are done to compare the mean square of reserve estimator between an individual loss model and an aggregate data model.