Full and 1‐year runoff risk in the credibility‐based additive loss reserving method

Abstract

In this paper, we consider the additive loss reserving (ALR) method in a Bayesian and credibility setup. The classical ALR method is a simple claims reserving method that combines prior information (e.g., premiums, number of contracts, market statistics) with claims observations. The Bayesian setup, which we present, in addition, allows for combining the information from a single runoff portfolio (e.g., company‐specific data) with the information from a collective (e.g., industry‐wide data) to analyze the claims reserves and the claims development result. However, in insurance practice, the associated distributions are usually unknown. Therefore, we do not follow the full Bayesian approach but apply credibility theory, which is distribution free and where we only need to know the first and second moments. That is, we derive the credibility predictors that minimize the expected squared loss within the class of affine‐linear functions of the observations (i.e., we derive linear Bayesian predictors). Using non‐informative priors, we link our credibility‐based ALR method to the classical ALR method and show that the credibility predictors coincide with the predictors in the classical ALR method. Moreover, we quantify the 1‐year risk and the full reserve risk by means of the conditional mean square error of prediction. Copyright © 2011 John Wiley & Sons, Ltd.