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Dependence modelling in multivariate claims run-off triangles

Published online by Cambridge University Press:  05 September 2012

Michael Merz ,
Mario V. Wüthrich  and
Enkelejd Hashorva
Michael Merz
Affiliation:
University of Hamburg, Department of Business Administration, 20146 Hamburg, Germany
Mario V. Wüthrich*
Affiliation:
ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland
Enkelejd Hashorva
Affiliation:
University of Lausanne, Department of Actuarial Science, HEC, 1015 Lausanne, Switzerland
*
*Correspondence to: Mario V. Wüthrich, ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland. E-mail: [email protected]
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Abstract

A central issue in claims reserving is the modelling of appropriate dependence structures. Most classical models cannot cope with this task. We define a multivariate log-normal model that allows to model both, dependence between different sub-portfolios and dependence within sub-portfolios such as claims inflation. In this model we derive closed form solutions for claims reserves and the corresponding prediction uncertainty.

Keywords

Claims reservingRun-off trianglesMultivariate claims trianglesAccounting year effectsCalendar year effectsClaims inflation
Type
Papers
Information
Annals of Actuarial Science , Volume 7 , Issue 1: Special issue on Enterprise Risk Management , March 2013 , pp. 3 - 25
Copyright
Copyright © Institute and Faculty of Actuaries 2012

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References

Barnett, G., Zehnwirth, B. (2000). Best estimates for reserves. Proceedings CAS, LXXXVII, 245–321.Google Scholar
Boyd, S., Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press.Google Scholar
Braun, C. (2004). The prediction error of the chain ladder method applied to correlated runoff triangles. ASTIN Bulletin, 34/2, 399–423.CrossRefGoogle Scholar
Brehm, P.J. (2002). Correlation and the aggregation of unpaid loss distributions. CAS Forum, 1–23.Google Scholar
Bühlmann, H., Gisler, A. (2005). A Course in Credibility Theory and its Applications. Springer.Google Scholar
Dahms, R. (2008). A loss reserving method for incomplete claim data. Bulletin Swiss Association of Actuaries, 2008, 127–148.Google Scholar
de Jong, P. (2006). Forecasting runoff triangles. North American Actuarial Journal, 10/2, 28–38.CrossRefGoogle Scholar
Donnelly, C., Wüthrich, M.V. (2012). Bayesian prediction of disability insurance frequencies using economic factors. Annals of Actuarial Science, 6/2, 381–400.Google Scholar
European Commission (2010). QIS5 Technical Specifications, Annex to Call for Advice from CEIOPS on QIS5.Google Scholar
Gigante, P., Picech, L., Sigalotti, L. (2012). Claims reserving in the hierarchical generalized linear models framework. Preprint.Google Scholar
Hertig, J. (1985). A statistical approach to the IBNR-reserves in marine insurance. ASTIN Bulletin, 15/2, 171–183.CrossRefGoogle Scholar
Johnson, R.A., Wichern, D.W. (1988). Applied Multivariate Statistical Analysis, 2nd edition. Prentice-Hall.Google Scholar
Kirschner, G.S., Kerley, C., Isaacs, B. (2008). Two approaches to calculating correlated reserves indications across multiple lines of business. Variance, 2/1, 15–38.Google Scholar
König, B., Weber, F., Wüthrich, M.V. (2011). Prediction of disability frequencies in life insurance. Zavarovalniški horizonti, Journal of Slovensko aktuarsko združenje, 7/3, 5–23.Google Scholar
Kuang, D., Nielsen, B., Nielsen, J.P. (2008). Forecasting with the age-period-cohort model and the extended chain-ladder model. Biometrika, 95, 987–991.Google Scholar
Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23/2, 213–225.Google Scholar
McNeil, A.J., Frey, R., Embrechts, P. (2005). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press.Google Scholar
Merz, M., Wüthrich, M.V. (2007). Prediction error of the chain ladder reserving method applied to correlated run-off triangles. Annals of Actuarial Science, 2/1, 25–50.CrossRefGoogle Scholar
Merz, M., Wüthrich, M.V. (2008a). Prediction error of the multivariate chain ladder reserving method. North American Actuarial Journal, 12/2, 175–197.Google Scholar
Merz, M., Wüthrich, M.V. (2008b). Modelling the claims development result for solvency purposes. CAS E-Forum, Fall 2008, 542–568.Google Scholar
Pestman, W.R. (1998). Mathematical Statistics. de Gruyter.Google Scholar
Saluz, A., Gisler, A., Wüthrich, M.V. (2011). Development pattern and prediction error for the stochastic Bornhuetter-Ferguson claims reserving method. ASTIN Bulletin, 41/2, 279–313.Google Scholar
Shi, P., Basu, S., Meyers, G.G. (2012). A Bayesian log-normal model for multivariate loss reserving. North American Actuarial Journal, 16/1, 29–51.Google Scholar
Shi, P., Frees, E.W. (2011). Dependent loss reserving using copulas. ASTIN Bulletin, 41/2, 449–486.Google Scholar
Swiss Solvency Test (2006). FINMA SST Technisches Dokument, Version 2. October 2006.Google Scholar
Wüthrich, M.V. (2010). Accounting year effects modelling in the stochastic chain ladder reserving method. North American Actuarial Journal, 14/2, 235–255.Google Scholar
Zhang, Y., Dukic, V., Guszcza, J. (2012). A Bayesian non-linear model for forecasting insurance loss payments. Journal Royal Statistical Society A, 175/2, 637–656.Google Scholar