Claims Reserving in Non-life Insurance: A Fully Bayesian Model

Abstract

Stochastic claims reserving has been developed mostly using models defined in the framework of the classical statistics. The recently proposed Time Series Chain Ladder (TSCL) is one of these models. In order to allow for a comparison with the Bayesian point of view, we propose a fully Bayesian model having the property of reproducing TSCL if improper priors are assumed. With “informative” priors the Bayesian model allows for incorporating into the reserving process relevant external data, e.g. expert opinions, which are largely used by the actuaries. We provide numerical examples using Markov Chain Monte Carlo methods.