Predictive Distributions of Outstanding Liabilities in General Insurance

TLDR

The paper extends England & Verrall’s 2002 methods to derive predictive distributions of outstanding general insurance liabilities using bootstrap or Bayesian techniques, noting Mack’s model is suitable for data with negative increments. Its purpose is to provide a way to obtain predictive distributions from recursive claims reserving models, including Mack’s 1993 model, thereby extending the original methodology. The authors develop a bootstrapping scheme and a Bayesian MCMC approach, modeling claims reserving with generalized linear models and recursive structures such as Mack’s model. Illustrative examples compare bootstrap and Bayesian predictive distributions, demonstrating the applicability and relative performance of both methods.

Abstract

ABSTRACT This paper extends the methods introduced in England & Verrall (2002), and shows how predictive distributions of outstanding liabilities in general insurance can be obtained using bootstrap or Bayesian techniques for clearly defined statistical models. A general procedure for bootstrapping is described, by extending the methods introduced in England & Verrall (1999), England (2002) and Pinheiro et al . (2003). The analogous Bayesian estimation procedure is implemented using Markov-chain Monte Carlo methods, where the models are constructed as Bayesian generalised linear models using the approach described by Dellaportas & Smith (1993). In particular, this paper describes a way of obtaining a predictive distribution from recursive claims reserving models, including the well known model introduced by Mack (1993). Mack's model is useful, since it can be used with data sets which exhibit negative incremental amounts. The techniques are illustrated with examples, and the resulting predictive distributions from both the bootstrap and Bayesian methods are compared.