  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.
