We propose a dependence-aware predictive modeling framework for multivariate risks stemmed from an insurance contract with bundling features - an important type of policy increasingly offered by major insurance companies. The bundling feature naturally leads to longitudinal measurements of multiple insurance risks, and correct pricing and management of such risks is of fundamental interest to financial stability of the macroeconomy. We build a novel predictive model that fully captures the dependence among the multivariate repeated risk measurements. Specifically, the longitudinal measurement of each individual risk is first modeled using pair copula construction with a D-vine structure, and the multiple D-vines are then integrated by a flexible copula. The proposed model provides a unified modeling framework for multivariate longitudinal data that can accommodate different scales of measurements, including continuous, discrete, and mixed observations, and thus can be potentially useful for various economic studies. A computationally efficient sequential method is proposed for model estimation and inference, and its performance is investigated both theoretically and via simulation studies. In the application, we examine multivariate bundled risks in multi-peril property insurance using proprietary data from a commercial property insurance provider. The proposed model is found to provide improved decision making for several key insurance operations. For underwriting, we show that the experience rate priced by the proposed model leads to a 9% lift in the insurer's net revenue. For reinsurance, we show that the insurer underestimates the risk of the retained insurance portfolio by 10% when ignoring the dependence among bundled insurance risks.

翻译：我们提出了一种依赖感知的预测建模框架，用于处理具有捆绑特征的保险合同产生的多变量风险——这是主要保险公司日益提供的一种重要保单类型。捆绑特征自然导致多种保险风险的纵向测量，而对此类风险的正确定价与管理对宏观经济金融稳定性具有根本重要性。我们构建了一个新颖的预测模型，能够完整捕捉多变量重复风险测量之间的依赖关系。具体而言，首先使用D藤结构的对偶Copula构造对每种个体风险的纵向测量进行建模，然后通过灵活的连接函数整合多个D藤。所提模型为多变量纵向数据提供了统一的建模框架，可适应包括连续型、离散型和混合型观测在内的不同测量尺度，因此潜在适用于多种经济研究。我们提出了一种计算高效的序贯方法进行模型估计与推断，并从理论上和通过模拟研究考察了其性能。在应用层面，我们使用某商业财产保险提供商的专有数据，研究了多险种财产保险中的多变量捆绑风险。结果表明，所提模型为几项关键保险运营提供了改进的决策支持。在承保方面，该模型定价的经验费率使保险公司净收入提升9%。在再保险方面，当忽略捆绑保险风险间的依赖关系时，保险公司对留存保险组合的风险低估了10%。