Flexible (panel) regression models for bivariate count-continuous data with an insurance application

We propose a flexible regression model that is suitable for mixed count-continuous panel data. The model is based on a compound Poisson representation of the continuous variable, with bivariate random effect following a polynomial-expansion-based joint density. Besides the distributional flexibility that it offers, the model allows for closed form forecast updating formulae. This property is especially important for insurance applications, in which the future individual insurance premium should be regularly updated according to one's own past claim history. An application to vehicle insurance claims is provided.