摘要
非寿险精算的核心问题之一是对未决赔款准备金进行准确评估。在未决赔款准备金评估中,多条业务线的流量三角形数据之间通常存在一定的相依关系。为了考虑不同业务线之间的相依关系对未决赔款准备金评估结果的影响,本文基于GB2分布建立了一种相依性准备金评估模型,该模型首先假设不同业务线的增量赔款服从GB2分布,并在分布的期望中引入事故年和进展年作为解释变量,引入日历年随机效应描述各条业务线之间的相依关系;然后借助贝叶斯HMC方法进行参数估计和未决赔款准备金预测,最后给出了总准备金的预测分布和评估结果。本文将该方法应用到两条业务线的流量三角形数据进行实证研究,并与现有其他方法进行了比较。实证研究结果表明,基于GB2分布的相依性准备金评估模型对未决赔款准备金的尾部风险和不确定性的考虑更加充分,更加适用于评估具有厚尾或者长尾特征的准备金数据。
One of the most critical problems in casualty insurance is to determine an appropriate outstanding reserve for incurred but unpaid losses. Forecasts and risk margins are often based on incremental or cumulative payment data corresponding to different business lines of loss triangles. Modeling dependency among multiple loss triangles has important implication for the determination of loss reserves in property and casualty insurance. In fact,owing to diversity of loss reserving data,it is critical to select the appropriate distribution.Generalized beta distribution of the second kind（ GB2 distribution） has a flexible probability density function with four parameters,which nests various distributions with light and heavy tails,to facilitate accurate loss reserving in insurance applications. This paper proposes a Bayesian model based on GB2 distribution to capture dependence between two cells of two different runoff triangles. First,we use the GB2 distribution to fit the incremental paid losses data and introduce accident year and development year as covariates. Then,we suppose a dependence between all the observations that belong to the same calendar year（ CY） for each line of business. This model can be done by using the calendar year as common random effect. For illustration,the model is applied to a dataset from Shi（ 2011） where a Bayesian method is proposed to estimate the distributionof the reserve. The result shows that the proposed model is more fully considered for the tail risk and uncertainty of the outstanding reserve than existing models,and is more suitable to model the loss reserving data with long and heavy tails.
出处
《统计研究》
CSSCI
北大核心
2018年第1期91-103,共13页
Statistical Research
基金
国家社会科学基金重大项目“巨灾保险的精算统计模型及其应用研究”(16ZDA052)
教育部人文社会科学重点研究基地重大项目“基于大数据的精算统计模型与风险管理问题研究”(16JJD910001)的资助
