考虑两类赔款数据相关性的随机性准备金进展法及改进

本文创新性地提出基于成对抽数的非参数Bootstrap方法、二元正态分布和Copulas函数三种考虑已决赔款与已报案赔款相关性的随机性准备金进展法，并结合非寿险精算实务中的经典流量三角形数据，应用R软件对三种考虑相关性的随机性准备金进展法进行了完整的编程实现，并模拟得到了最终损失、未决赔款准备金和IBNR的完整的预测分布。本文提出的考虑相关性的随机性准备金进展法不但考虑了两类赔款数据之间的相关性，而且体现了不同事故年已发生已报案未决赔款准备金进展情况之间的差异。这种处理相关性的思路和方法在多元准备金评估中具有重要的应用价值。

Stochastic Reserves Development Methods Based on the Correlation Among Paid-Incurred Payments Data and Their Improvement

Three stochastic reserves development methods are innovatively proposed in this paper considering the correlation between paid-incurred payments data, i.e. based on non-parametric Bootstrap method with pairwise resampling, based on bivariate normal distribution, and based on Copulas function. Combined the classic run-off triangles data in the non-life actuarial practice, a complete programming for three stochastic reserve development methods is provided based on the correlation with R software. Further, the complete predictive distributions of ultimate loss, outstanding claims reserves and IBNR are simulated. The proposed stochastic reserve development methods based on the correlation not only consider the correlation between the paid payments and the incurred payments, but also reflect the development difference of incurred and reported outstanding claims reserves in different accident years. Such ideas and methods considering correlation have important theoretical significance and practical value for multivariate reserving.