Loss development modelling is the actuarial practice of predicting the total 'ultimate' losses incurred on a set of policies once all claims are reported and settled. This poses a challenging prediction task as losses frequently take years to fully emerge from reported claims, and not all claims might yet be reported. Loss development models frequently estimate a set of 'link ratios' from insurance loss triangles, which are multiplicative factors transforming losses at one time point to ultimate. However, link ratios estimated using classical methods typically underestimate ultimate losses and cannot be extrapolated outside the domains of the triangle, requiring extension by 'tail factors' from another model. Although flexible, this two-step process relies on subjective decision points that might bias inference. Methods that jointly estimate 'body' link ratios and smooth tail factors offer an attractive alternative. This paper proposes a novel application of Bayesian hidden Markov models to loss development modelling, where discrete, latent states representing body and tail processes are automatically learned from the data. The hidden Markov development model is found to perform comparably to, and frequently better than, the two-step approach on numerical examples and industry datasets.

翻译：损失进展建模是一种精算实践，旨在预测一组保单在所有索赔均已报告和结案后所产生的最终总损失。这是一项具有挑战性的预测任务，因为损失通常需要数年时间才能从已报告的索赔中完全显现，并且并非所有索赔都已报告。损失进展模型通常从保险损失三角形中估计一组"连接比"，这些连接比是将某一时间点的损失转换为最终损失的乘性因子。然而，使用经典方法估计的连接比通常会低估最终损失，并且无法在三角形区域之外进行外推，需要借助来自另一个模型的"尾部因子"进行扩展。尽管灵活，但这种两步法依赖于可能使推断产生偏差的主观决策点。能够联合估计"主体"连接比和平滑尾部因子的方法提供了一种有吸引力的替代方案。本文提出了一种贝叶斯隐马尔可夫模型在损失进展建模中的新颖应用，其中代表主体和尾部过程的离散潜在状态可从数据中自动学习。在数值示例和行业数据集上的实验表明，隐马尔可夫进展模型的性能与两步法相当，且通常更优。