This paper focuses on modelling loss reserving to pay outstanding claims. As the amount liable on any given claim is not known until settlement, we propose a flexible model via heavy-tailed and skewed distributions to deal with outstanding liabilities. The inference relies on Markov chain Monte Carlo via Gibbs sampler with adaptive Metropolis algorithm steps allowing for fast computations and providing efficient algorithms. An illustrative example emulates a typical dataset based on a runoff triangle and investigates the properties of the proposed models. Also, a case study is considered and shows that the proposed model outperforms the usual loss reserving models well established in the literature in the presence of skewness and heavy tails.

翻译：本文聚焦于为支付未决赔款而建立的损失准备金模型。由于任何给定索赔的应计金额在结算前无法确定，我们提出了一种基于厚尾分布与偏斜分布的灵活模型来处理未决负债。推断过程采用基于吉布斯采样的马尔可夫链蒙特卡洛方法，结合自适应梅特罗波利斯算法步骤，实现了快速计算并提供了高效算法。一个示例基于流量三角形模拟典型数据集，验证了所提模型的特性。此外，通过案例研究表明，在数据存在偏斜性与厚尾特征时，所提模型优于文献中已建立的常规损失准备金模型。