A Bayesian Skew-heavy-tailed modelling for loss reserving

Abstract

This paper focuses on modelling loss reserving to pay outstanding claims. As the amount liable on any given claim is not known until settlement, we propose a flexible model via heavy-tailed and skewed distributions to deal with outstanding liabilities. The inference relies on Markov chain Monte Carlo via Gibbs sampler with adaptive Metropolis algorithm steps allowing for fast computations and providing efficient algorithms. An illustrative example emulates a typical dataset based on a runoff triangle and investigates the properties of the proposed models. Also, a case study is considered and shows that the proposed model outperforms the usual loss reserving models well established in the literature in the presence of skewness and heavy tails.