One-Year and Full Reserve Risk for the Bayesian Additive Loss Reserving Method

In this paper we consider the additive loss reserving (ALR) method in a Bayesian set up. The classical ALR method is a simple claims reserving method which combines prior information (e.g. premium, number of contracts, market statistics) and claims observations. The presented Bayesian set up allows in addition for combining the information from a single run-off 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. We derive credibility predictors and analyze their properties within this Bayesian framework. Using non-informative priors we link to the classical ALR method and show that the credibility predictors coincide with the predictors in the classical ALR method. Moreover, we quantify the one-year and the full reserve risk by the conditional mean square error of prediction.