Predictive Modeling of Multivariate Longitudinal Insurance Claims Using Pair Copula Construction

The bundling feature of a nonlife insurance contract often leads to multiple longitudinal measurements of an insurance risk. Assessing the association among the evolution of the multivariate outcomes is critical to the operation of property-casualty insurers. One complication in the modeling process is the non-continuousness of insurance risks. Motivated by insurance applications, we propose a general framework for modeling multivariate repeated measurements. The framework easily accommodates different types of data, including continuous, discrete, as well as mixed outcomes. Specifically, the longitudinal observations of each response is separately modeled using pair copula constructions with a D-vine structure. The multiple D-vines are then joined by a multivariate copula. A sequential approach is employed for inference and its performance is investigated under a simulated setting. In the empirical analysis, we examine property risks in a government multi-peril property insurance program. The proposed method is applied to both policyholders’ claim count and loss cost. The model is validated based on out-of-sample predictions.