Full Bayesian Analysis of Claims Reserving Uncertainty

Abstract

We revisit the gamma-gamma Bayesian chain-ladder (BCL) model for claims reserving in non-life insurance. This claims reserving model is usually used in an empirical Bayesian way using plug-in estimates for variance parameters, because this empirical Bayesian framework allows us for closed form solutions. The main purpose of this paper is to develop the full Bayesian case also considering prior distributions for variance parameters, and to study the resulting sensitivities.

Keywords: Chain-Ladder Method, Claims Reserving Uncertainty, Claims Development Result, Mack's Formula, Merz-WüThrich's Formula, Conditional Mean Square Error of Prediction, Runoff Uncertainty, Full Bayesian Chain-Ladder Model

JEL Classification: G22