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. While our analysis mainly focuses on multivariate insurance risks, the proposed model indeed contributes to the broad research area of longitudinal data analysis. In particular, it 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.

中文翻译：

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使用配对联结构造通过依赖感知预测增强捆绑保险风险的定价和管理

我们提出了一种依赖感知预测模型框架，用于处理源于具有捆绑功能的保险合同的多变量风险——这是大型保险公司越来越多地提供的一种重要保单类型。捆绑特性自然会导致多种保险风险的纵向衡量，而对此类风险的正确定价和管理对于宏观经济的金融稳定至关重要。我们建立了一个新颖的预测模型，可以充分捕捉多变量重复风险测量之间的依赖性。具体来说，首先使用具有 D-vine 结构的配对 copula 结构对每个单独风险的纵向测量进行建模，然后通过灵活的 copula 集成多个 D-vine。虽然我们的分析主要集中在多元保险风险上，但所提出的模型确实有助于纵向数据分析的广泛研究领域。特别是，它为多元纵向数据提供了一个统一的建模框架，可以适应不同尺度的测量，包括连续、离散和混合观测，因此可能对各种经济研究有用。提出了一种计算高效的顺序方法用于模型估计和推理，并通过理论和仿真研究对其性能进行了研究。在该应用程序中，我们使用商业财产保险提供商的专有数据检查多险财产保险中的多变量捆绑风险。研究发现，所提出的模型可以为几个关键的保险业务提供改进的决策。对于承保，我们表明所提出的模型定价的经验费率使保险公司的净收入提高了 9%。对于再保险，我们发现，当忽略捆绑保险风险之间的依赖性时，保险公司将保留保险组合的风险低估了 10%。