A multivariate micro-level insurance counts model with a Cox process approach

04/23/2020 ∙ by Benjamin Avanzi, et al. ∙ 0

In this paper, we focus on estimating ultimate claim counts in multiple insurance processes and thus extend the associated literature of micro-level stochastic reserving models to the multivariate context. Specifically, we develop a multivariate Cox process to model the joint arrival process of insurance claims in multiple Lines of Business. The dependency structure is introduced via multivariate shot noise intensity processes which are connected with the help of Lévy copulas. Such a construction is more parsimonious and tractable in higher dimensions than plain vanilla common shock models. We also consider practical implementation and explicitly incorporate known covariates, such as seasonality patterns and trends, which may explain some of the relationship between two insurance processes (or at least help tease out those relationships). We develop a filtering algorithm based on the reversible-jump Markov Chain Monte Carlo (RJMCMC) method to estimate the unobservable stochastic intensities. Model calibration is illustrated using real data from the AUSI data set.

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