The Mean Square Error of Prediction in the Chain Ladder Reserving Method – A Comment

Thomas Mack; Gerhard Quarg; Christian Braun

doi:10.2143/AST.36.2.2017937

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We discuss some questionable points of the approach taken in the paper by Buchwalder, Bühlmann, Merz and Wüthrich and come to the conclusion that this approach does not yield an improvement of Mack’s original formula. The main reason is that the new approach disregards the negative correlation of the squares of the development factors. The same applies to the formula by Murphy (PCAS 1994).

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Merz, M. and Wüthrich, M. V. 2007. Prediction Error of the Chain Ladder Reserving Method applied to Correlated Run-off Triangles. Annals of Actuarial Science, Vol. 2, Issue. 1, p. 25.

Merz, Michael and Wüthrich, Mario V. 2007. Mittlerer quadratischer Prognosefehler bei der Prognose des Abwicklungsergebnisses mittels der Chain-Ladder-Methode. Zeitschrift für die gesamte Versicherungswissenschaft, Vol. 96, Issue. S1, p. 207.

Heberle, Jochen Huergo, Luis and Merz, Michael 2008. Prognose des Abwicklungsergebnisses mittels Chain-Ladder-Verfahren für abhängige Run-Off-Portfolios. Zeitschrift für die gesamte Versicherungswissenschaft, Vol. 97, Issue. 4, p. 439.

Merz, Michael and Wüthrich, Mario V. 2008. Prediction Error of the Multivariate Chain Ladder Reserving Method. North American Actuarial Journal, Vol. 12, Issue. 2, p. 175.

Wüthrich, Mario V. 2008. Prediction error in the chain ladder method. Insurance: Mathematics and Economics, Vol. 42, Issue. 1, p. 378.

Wüthrich, Mario V. Merz, Michael and Bühlmann, Hans 2008. Bounds on the estimation error in the chain ladder method. Scandinavian Actuarial Journal, Vol. 2008, Issue. 4, p. 283.

Gisler, Alois and Wüthrich, Mario V. 2008. Credibility for the Chain Ladder Reserving Method. ASTIN Bulletin, Vol. 38, Issue. 2, p. 565.

Verdonck, Tim Van Wouwe, Martine and Dhaene, Jan 2009. A Robustification of the Chain-Ladder Method. North American Actuarial Journal, Vol. 13, Issue. 2, p. 280.

Liu, Huijuan and Verrall, Richard 2009. Predictive Distributions for Reserves which Separate True IBNR and IBNER Claims. ASTIN Bulletin, Vol. 39, Issue. 1, p. 35.

Alai, D. H. Merz, M. and Wüthrich, M. V. 2009. Mean Square Error of Prediction in the Bornhuetter–Ferguson Claims Reserving Method. Annals of Actuarial Science, Vol. 4, Issue. 1, p. 7.

Wüthrich, Mario V. Merz, Michael and Lysenko, Natalia 2009. Uncertainty of the claims development result in the chain ladder method. Scandinavian Actuarial Journal, Vol. 2009, Issue. 1, p. 63.

Björkwall, Susanna Hössjer, Ola and Ohlsson, Esbjörn 2009. Non-parametric and parametric bootstrap techniques for age-to-age development factor methods in stochastic claims reserving. Scandinavian Actuarial Journal, Vol. 2009, Issue. 4, p. 306.

Jessen, Anders Hedegaard Mikosch, Thomas and Samorodnitsky, Gennady 2011. Prediction of outstanding payments in a Poisson cluster model. Scandinavian Actuarial Journal, Vol. 2011, Issue. 3, p. 214.

Alai, D. H. Merz, M. and Wüthrich, M. V. 2011. Prediction Uncertainty in the Bornhuetter-Ferguson Claims Reserving Method: Revisited. Annals of Actuarial Science, Vol. 5, Issue. 1, p. 7.

2012. Stochastic Claims Reserving Methods in Insurance. p. 409.

Riegel, Ulrich 2014. A BIFURCATION APPROACH FOR ATTRITIONAL AND LARGE LOSSES IN CHAIN LADDER CALCULATIONS. ASTIN Bulletin, Vol. 44, Issue. 1, p. 127.

Peremans, Kris Segaert, Pieter Van Aelst, Stefan and Verdonck, Tim 2017. Robust bootstrap procedures for the chain-ladder method. Scandinavian Actuarial Journal, Vol. 2017, Issue. 10, p. 870.

Tuysuz, Sukriye and Pekel, Pervin 2017. A Comparison of Stochastic Claims Reserving Methods. SSRN Electronic Journal ,

Siegenthaler, Filippo 2020. The Prediction Uncertainties in the Chain-Ladder Model of Mack: Building on the Latest Gisler Developments. SSRN Electronic Journal ,

Engler, Nils and Lindskog, Filip 2024. Mack’s estimator motivated by large exposure asymptotics in a compound poisson setting. ASTIN Bulletin, Vol. 54, Issue. 2, p. 310.

Article contents

The Mean Square Error of Prediction in the Chain Ladder Reserving Method – A Comment

Abstract

References

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

The Mean Square Error of Prediction in the Chain Ladder Reserving Method – A Comment

Abstract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests