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INDIVIDUAL LOSS RESERVING WITH THE MULTIVARIATE SKEW NORMAL FRAMEWORK

Published online by Cambridge University Press:  06 August 2013

Mathieu Pigeon ,
Katrien Antonio  and
Michel Denuit
Mathieu Pigeon*
Affiliation:
Université Catholique de Louvain, UCL, Belgium
Katrien Antonio
Affiliation:
KU Leuven, Belgium and University of Amsterdam, UvA, The Netherlands E-Mail: [email protected]
Michel Denuit
Affiliation:
Université Catholique de Louvain, UCL, Belgium E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

The evaluation of future cash flows and solvency capital recently gained importance in general insurance. To assist in this process, our paper proposes a novel loss reserving model, designed for individual claims developing in discrete time. We model the occurrence of claims, as well as their reporting delay, the time to the first payment, and the cash flows in the development process. Our approach uses development factors similar to those of the well-known chain–ladder method. We suggest the Multivariate Skew Normal distribution as a multivariate distribution suitable for modeling these development factors. Empirical analysis using a real portfolio and out-of-sample prediction tests demonstrate the relevance of the model proposed.

Keywords

Stochastic loss reservinggeneral insuranceMultivariate Skew Normal distributionchain–ladderindividual claims
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 3 , September 2013 , pp. 399 - 428
Copyright
Copyright © ASTIN Bulletin 2013 

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References

Akdemir, D. (2009) A Class of Multivariate Skew Distributions: Properties and Inferential Issues. PhD thesis, Bowling Green State University, Ohio.Google Scholar
Akdemir, D. and Gupta, A.K. (2010) A matrix variate skew distribution. European Journal of Pure and Applied Mathematics, 3 (2), 128–140.Google Scholar
Antonio, K. and Plat, R. (2013) Micro–level stochastic loss reserving for general insurance. Scandinavian Actuarial Journal, DOI:10.1080/03461238.2012.755938.Google Scholar
Arjas, E. (1989) The claims reserving problem in non–life insurance: Some structural ideas. ASTIN Bulletin, 19 (2), 139–152.CrossRefGoogle Scholar
Azzalini, A. (1985) A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171–178.Google Scholar
Brouhns, N., Denuit, M. and Vermunt, J. K. (2002) A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31, 373–393.Google Scholar
Cheng, J.T. and Amin, N.A.K. (1983) Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 45 (3), 394–403.Google Scholar
Drieskens, D., Henry, M., Walhin, J.-F. and Wielandts, J. (2012) Stochastic projection for large individual losses. Scandinavian Actuarial Journal, 1, 1–39.CrossRefGoogle Scholar
England, P.D. and Verrall, R.J. (2002) Stochastic claims reserving in general insurance. British Actuarial Journal, 8, 443–544.CrossRefGoogle Scholar
Gupta, A.K. and Chen, J.T. (2004) A class of multivariate skew normal models. The Annals of the Institute of Statistical Mathematics, 56 (2), 305–315.CrossRefGoogle Scholar
Happ, S. and Wüthrich, M. (2013) Paid–incurred chain reserving method with dependence modelling. ASTIN Bulletin, 43 (1), 1–20.CrossRefGoogle Scholar
Mack, T. (1993) Distribution–free calculation of the standard error of chain–ladder reserve estimates. ASTIN Bulletin, 23 (2), 213–225.CrossRefGoogle Scholar
Mack, T. (1999) The standard error of chain–ladder reserve estimates: Recursive calculation and inclusion of a tail-factor. ASTIN Bulletin, 29, 361–366.CrossRefGoogle Scholar
Martinez, M.D., Nielsen, B., Nielsen, J.P. and Verrall, R.J. (2011) Cash flow simulation for a model of outstanding liabilities based on claim amounts and claim numbers. ASTIN Bulletin, 41 (1), 107–129.Google Scholar
Martinez, M.D., Nielsen, J.P. and Verrall, R.J. (2012) Double chain–ladder. ASTIN Bulletin, 42 (1), 59–76.Google Scholar
Merz, M. and Wüthrich, M.V. (2010) PIC claims reserving method. Insurance: Mathematics and Economics, 46 (3), 568–579.Google Scholar
Murphy, K. and McLennan, A. (2006) A method for projecting individual large claims. Casualty Actuarial Society Forum, Fall Forum, 205–236.Google Scholar
Norberg, R. (1993) Prediction of outstanding liabilities in non-life insurance. ASTIN Bulletin, 23 (1), 95–115.CrossRefGoogle Scholar
Norberg, R. (1999) Prediction of outstanding liabilities II. Model extensions variations and extensions. ASTIN Bulletin, 29 (1), 5–25.CrossRefGoogle Scholar
Pigeon, M. and Denuit, M. (2011) Composite lognormal-pareto model with random threshold. Scandinavian Actuarial Journal, 3, 177–192.CrossRefGoogle Scholar
Ranneby, B. (1984) The maximum spacing method. An estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics, 11 (2), 93–112.Google Scholar
Roberts, C. and Geisser, S. (1966) A necessary and sufficient condition for the square of a random variable to be gamma. Biometrika, 53 (1/2), 275–278.CrossRefGoogle ScholarPubMed
Rosenlund, S. (2012) Bootstrapping individual claim histories. ASTIN Bulletin,42 (1), 291–324.Google Scholar
Verrall, R., Nielsen, J.P. and Jessen, A. (2010) Including count data in claims reserving. ASTIN Bulletin, 40 (2), 871–887.Google Scholar
Wüthrich, M.V. and Merz, M. (2008) Stochastic Claims Reserving Methods in Insurance. Chichester, England: Wiley Finance.Google Scholar
Zhao, X.B., Zhou, X. and Wang, J.L. (2009) Semiparametric model for prediction of individual claim loss reserving. Insurance: Mathematics and Economics, 45 (1), 1–8.Google Scholar