Casualty insurance-linked securities (ILS) are appealing to investors because the underlying insurance claims, which are directly related to resulting security performance, are uncorrelated with most other asset classes. Conversely, casualty ILS are appealing to insurers as an efficient capital managment tool. However, securitizing casualty insurance risk is non-trivial, as it requires forecasting loss ratios for pools of insurance policies that have not yet been written, in addition to estimating how the underlying losses will develop over time within future accident years. In this paper, we lay out a Bayesian workflow that tackles these complexities by using: (1) theoretically informed time-series and state-space models to capture how loss ratios develop and change over time; (2) historic industry data to inform prior distributions of models fit to individual programs; (3) stacking to combine loss ratio predictions from candidate models, and (4) both prior predictive simulations and simulation-based calibration to aid model specification. Using historic Schedule P filings, we then show how our proposed Bayesian workflow can be used to assess and compare models across a variety of key model performance metrics evaluated on future accident year losses.

翻译：财产保险连接证券（ILS）对投资者具有吸引力，因为其基础保险索赔与证券表现直接相关，且与大多数其他资产类别无关。反之，财产保险连接证券对保险公司而言是一种高效的资本管理工具。然而，财产保险风险的证券化并非易事，它需要预测尚未承保的保单组合的损失率，并估计基础损失在未来事故年度内随时间的发展情况。本文提出了一种贝叶斯工作流，通过以下方式应对这些复杂性：（1）使用理论驱动的时间序列和状态空间模型捕捉损失率随时间发展和变化的规律；（2）利用历史行业数据为适用于单个项目的模型先验分布提供信息；（3）通过堆叠法整合候选模型的损失率预测结果，以及（4）运用先验预测模拟和基于模拟的校准辅助模型设定。基于历史Schedule P申报数据，我们进一步展示了所提出的贝叶斯工作流如何用于评估和比较模型在未来事故年度损失上的多种关键性能指标。