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Individual Loss Reserving with the Multivariate Skew Normal Framework

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Pigeon, Mathieu [UCL] Antonio, Katrien Denuit, Michel [UCL]

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 SkewNormal distribution as amultivariate 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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2013
Language Anglais
Journal information "ASTIN Bulletin" - Vol. 43, no. 3, p. 399-428 (2013)
Peer reviewed yes
issn 0515-0361
e-issn 1783-1350
Publication status Publié
Affiliation UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords Stochastic loss reserving ; general insurance ; Multivariate Skew Normal distribution ; chain–ladder ; individual claims
Links
  1. European Journal of Pure and Applied Mathematics, 3, 128 (2010)
  2. ARJAS Elia, The Claims Reserving Problem in Non-Life Insurance, 10.2143/ast.19.2.2014905
  3. Scandinavian Journal of Statistics, 12, 171 (1985)
  4. Brouhns Natacha, Denuit Michel, Vermunt Jeroen K., A Poisson log-bilinear regression approach to the construction of projected lifetables, 10.1016/s0167-6687(02)00185-3
  5. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 45, 394 (1983)
  6. Scandinavian Actuarial Journal, 1, 1 (2012)
  7. England P.D., Verrall R.J., Stochastic Claims Reserving in General Insurance, 10.1017/s1357321700003809
  8. Gupta Arjun K., Chen John T., A class of multivariate skew-normal models, 10.1007/bf02530547
  9. Happ Sebastian, Wüthrich Mario V., Paid-Incurred Chain Reserving Method with Dependence Modeling, 10.1017/asb.2012.4
  10. Mack Thomas, Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates , 10.2143/ast.23.2.2005092
  11. Mack Thomas, The Standard Error of Chain Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor , 10.2143/ast.29.2.504622
  12. ASTIN Bulletin, 41, 107 (2011)
  13. ASTIN Bulletin, 42, 59 (2012)
  14. Merz Michael, Wüthrich Mario V., Paid–incurred chain claims reserving method, 10.1016/j.insmatheco.2010.02.004
  15. Norberg Ragnar, Prediction of Outstanding Liabilities in Non-Life Insurance , 10.2143/ast.23.1.2005103
  16. Norberg Ragnar, Prediction of Outstanding Liabilities II. Model Variations and Extensions , 10.2143/ast.29.1.504603
  17. Scandinavian Actuarial Journal, 3, 177 (2011)
  18. Scandinavian Journal of Statistics, 11, 93 (1984)
  19. Roberts Charles, Geisser Seymour, A Necessary and Sufficient Condition for the Square of a Random Variable to be Gamma, 10.2307/2334082
  20. ASTIN Bulletin, 42, 291 (2012)
  21. ASTIN Bulletin, 40, 871 (2010)
  22. Stochastic Claims Reserving Methods in Insurance (2008)
  23. Zhao Xiao Bing, Zhou Xian, Wang Jing Long, Semiparametric model for prediction of individual claim loss reserving, 10.1016/j.insmatheco.2009.02.009
Bibliographic reference Pigeon, Mathieu ; Antonio, Katrien ; Denuit, Michel. Individual Loss Reserving with the Multivariate Skew Normal Framework. In: ASTIN Bulletin, Vol. 43, no. 3, p. 399-428 (2013)
Permanent URL http://hdl.handle.net/2078.1/133642