Dependence modeling of multivariate longitudinal hybrid insurance data with dropout

Financial services industries, such as insurance, increasingly use data from their broad cross-section of customers and follow these customers over time. In other areas such as medicine, engineering, and communication systems, it is well known that following subjects over time may result in biased data, for example, the so-called ”dropout effect”. This paper introduces techniques to address dropout commonly encountered in the insurance domain. Specifically, in the insurance context, multivariate claims outcomes may be related to a customer's dropout or decision to lapse a policy. Insurance claims outcomes are also naturally a hybrid with both discrete and continuous components, which adds complexity to model calibration. Decision makers in the insurance industry will find our work provides helpful guidance in integrating customer loyalty, especially with bundled coverages. This paper introduces a generalized method of moments technique to estimate dependence parameters where associations are represented using copulas. This is especially useful for large data sets. The paper describes how the joint model provides new information that insurers can use to better manage their portfolios of risks. An application to a Spanish insurer data set is presented.