基于相依结构的多元索赔准备金评估随机性方法研究评述

A Review on Multivariate Stochastic Claims Reserving Methods with Dependence Structures

索赔准备金评估方法的最新发展趋势是考虑相依结构的两类多元评估随机性方法,即将基于已决与已报案赔款之间的相关性、基于不同业务线之间的相依性体现在准备金评估的分析框架中。首先系统梳理两类多元评估随机性方法的最新进展,将一元评估方法的三个层次(无分布假设、分布模型假设、在分层结构下考虑各种分布假设)扩展到两类多元评估方法中。在多元框架下,将多元统计分析方法、精算学中的相依风险建模方法(多元分布模型、概率联结函数、共单调技术)应用到这三个层次中,探讨索赔准备金的均值和预测均方误差估计、预测分布的模拟问题。其次扩展考虑一元和多元框架下日益受到关注的含索赔通胀和会计年相依性问题。最后探讨这些评估方法在国外偿付能力监管中的应用。这将进一步拓展准备金评估不确定性风险度量的研究,推动精算学中定量风险管理技术的发展。

The latest development trend of claims reserving is the advances in two types of multivariate stochastic claims reserving methods with dependence structures, where the correlation of paid and incurred claims data and the dependencies among multiple lines of business are incorporated into an analytical framework of aggregate claims re- serving models respectively. The paper collated and summarized the latest developments of multivariate stochastic claims reserving methods. Based on the aforementioned investigations, the proposed three levels of univariate sto- chastic claims reserving methods （i. e. distribution-free assumptions, distribution model assumptions, and various distribution assumptions within hierarchical structure） are to be extended to the studies of the two types of multivari- ate stochastic claims reserving methods in this paper. In the multivariate framework, by incorporating multivariate statistical analysis methods and dependent risk modeling methods （such as multivariate distribution models, copula functions, comonotonicity techniques） into these three levels, we investigated the mean estimates,mean square error of prediction, and simulated predictive distributions of claims reserves. The paper considered further to extend the dependencies as regards to claims inflation and accounting year effects, which were concerned increasingly in both univariate and multivariate framework. Finally, the latest exploration and application of these reserving methods in foreign solvency regulation were discussed. These exploratory studies will further expand the scope of the uncertainty risk measure of claims reserving, which are expected to have significant contributions in promoting the quantitative risk management techniques of actuarial science.