Recent years have seen rapid increase in the application of machine learning to insurance loss reserving. They yield most value when applied to large data sets, such as individual claims, or large claim triangles. In short, they are likely to be useful in the analysis of any data set whose volume is sufficient to obscure a naked-eye view of its features. Unfortunately, such large data sets are in short supply in the actuarial literature. Accordingly, one needs to turn to synthetic data. Although the ultimate objective of these methods is application to real data, the use of synthetic data containing features commonly observed in real data is also to be encouraged.
While there are a number of claims simulators in existence, each valuable within its own context, the inclusion of a number of desirable (but complicated) data features requires further development. Accordingly, in this paper we review those desirable features, and propose a new simulator of individual claim experience called `SynthETIC`.
Our simulator is publicly available, open source, and fills a gap in the non-life actuarial toolkit. The simulator specifically allows for desirable (but optionally complicated) data features typically occurring in practice, such as variations in rates of settlements and development patterns; as with superimposed inflation, and various discontinuities, and also enables various dependencies between variables. The user has full control of the mechanics of the evolution of an individual claim. As a result, the complexity of the data set generated (meaning the level of difficulty of analysis) may be dialled anywhere from extremely simple to extremely complex.
A Copula Based Bayesian Approach for Paid-Incurred Claims Models for Non-Life Insurance Reserving
我们的文章认为，最近开发的随机模型，结合索赔支付和发生的损失信息到一个连贯的准备金方法。特别地，我们结合Hertig et al.（1985）和Gogol et al.（1993）的索赔准备金模型，发展了一个分层贝叶斯支付-发生-索赔模型族。在这个过程中，我们扩展了Merz等人（2010）的独立对数正态模型，通过使用数据增强混合Copula支付-发生索赔模型来合并不同的依赖结构。将支付和已发生的损失纳入未偿损失负债和由此产生的准备金的完整预测分布的估计中的效用和影响在以下情况下得到证明：（i）独立支付（P）数据模型;（ii）Merz等人（2010）的独立支付-已发生索赔（PIC）数据模型;（iii）一种新的相关滞后年伸缩块对角高斯Copula PIC数据模型，通过变换结合共轭;（iv）一种新的数据增强混合阿基米德Copula相关PIC数据模型。通过一类自适应马尔可夫链蒙特卡罗抽样算法，在这样的模型中的推理。这些方法结合了一个数据增强框架，用于有效地评估基于Copula的PIC模型在损失预留三角形中的可能性。自适应策略基于由对称矩阵的指数表示正定协方差矩阵，如Leonard等人（1992）所提出的。
Asymptotics of Systemic Risk in a Renewal Model with Multiple Business Lines and Heterogeneous Claims
School of Big Data and Statistics, Anhui University（安徽大学大数据与统计学院）；School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）
