Recursive Credibility Formula for Chain Ladder Factors and the Claims Development Result

In recent Solvency II considerations much effort has been put into the development of appropriate models for the study of the one-year loss reserving uncertainty in non-life insurance. In this article we derive formulas for the conditional mean square error of prediction of the one-year claims development result in the context of the Bayes chain ladder model studied in Gisler-Wüthrich [9]. The key to these formulas is a recursive representation for the results obtained in Gisler-Wüthrich [9].

Keywords Claims reserving, chain ladder method, credibility chain ladder method, claims development result, year end expectation, loss experience prior accident years, liability at maturity, solvency, mean square error of prediction.