Robustness of Tweedie Model of Reserves with Respect to Distribution of Severity of Claims

• Autorzy: Agata Boratyńska , Dorota Juszczak
• Języki publikacji: EN

Abstrakty

EN

The aim of the work is to discuss the robustness of estimation procedures and robustness of prediction in Tweedie's compound Poisson model. This model is applied to the claim reserving problem. The quality of parameter estimators and predictors is studied when the distribution of severity of claims is disturbed. The ε-contamination class of distributions is considered. The example, where errors of estimators are large is presented. The simulation methods, using the R programming environment, are applied.(original abstract)

Słowa kluczowe

EN

Estimation; Moments of gamma distribution; Linear models; Mathematical statistics

PL

Estymacja; Momenty rozkładu gamma; Modele liniowe; Statystyka matematyczna

• Czasopismo: Metody Ilościowe w Badaniach Ekonomicznych / Szkoła Główna Gospodarstwa Wiejskiego
• Rocznik: 2015
• Tom: 16(XVI)
• Numer: nr 1
• Strony: 53--74

Twórcy

autor

Agata Boratyńska

• Szkoła Główna Handlowa w Warszawie

autor

Dorota Juszczak

• Szkoła Główna Handlowa w Warszawie

Bibliografia

• Antonio K., Beirlant J. (2007) Actuarial statistics with generalized linear mixed models, Insurance: Mathematics and Economics 40(1), 58-76.
• Bornhuetter R. L., Ferguson R. E. (1972) The actuary and IBNR. Proceedings of the Casualty Actuarial Soc. 59, 181-195.
• Boucher J. P., Davidov D. (2011) On the Importance of Dispersion Modeling for Claims Reserving: An Application with the Tweedie Distribution, Variance 5(2), 158-172.
• England P. D., Verrall R. J. (1999) Analytic and bootstrap estimates of prediction errors in claims reserving, Insurance: Mathematics and Economics 25(3), 281-293.
• England P. D., Verrall R. J. (2002) Stochastic claims reserving in general insurance, British Actuarial Journal 8(3), 443-518.
• Gisler A., Wüthrich M. V. (2008) Credibility for the Chain Ladder Reserving Method, ASTIN Bulletin 38(2), 565-600.
• Hampel F. R., Ronchetti E. M., Rousseeuw P. J., Stahel W. A. (1986) Robust statistics: the approach based on influence functions. Wiley, New York.
• Han Z., Gau W. (2008) Estimation of loss reserves with lognormal development factors, Insurance: Mathematics and Economics 42(1), 389-395.
• Huber P. J. (1981) Robust statistics. Wiley, New York.
• Jasiulewicz H. (2013) Przestrzeń stanów i filtr Kalmana w teorii ubezpieczeń, Roczniki Kolegium Analiz Ekonomicznych z. 34, Oficyna Wydawnicza SGH, Warszawa, 101-116.
• Jørgensen B. (1997) The Theory of Dispersion Model, Chapman and Hall, London.
• Jørgensen B., de Souza M. C. P. (1994) Fitting Tweedie's Compound Poisson Model to Insurance Claims Data, Scandinavian Actuarial Journal 1, 69-93.
• Liu H., Verrall R. J. (2009) A Bootstrap Estimate of the Predictive Distribution of Outstanding Claims for the Schnieper Model, ASTIN Bulletin 39(2), 677-689.
• Mack T. (1991) A simple parametric model for rating automobile insurance or estimating IBNR claims reserves, ASTIN Bulletin 21(1), 93-109.
• Mack T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates, ASTIN Bulletin 23(2), 213-225.
• Mack T. (1999) The standard error of chain ladder reserve estimates: recursive calculation and inclusion of a tail factor, ASTIN Bulletin 29, 361-366.
• Ntzoufras I., Dellaportas P. (2002) Bayesian Modelling of Outstanding Liabilities Incorporating Claim Count Uncertainty, North American Actuarial Journal 6(1), 113-128.
• Ohlsson E., Johansson B. (2006) Exact credibility and Tweedie models, ASTIN Bulletin 36(1), 121-133.
• Peters G. W., Shevchenko P. V., Wüthrich M. V. (2009) Model uncertainty in claims reserving within Tweedie's compound Poisson models, ASTIN Bulletin 39(1), 1-33.
• Sánchez J. R., Vilar J. L. (2011) Bayesian and credibility estimation for the chain ladder reserving method, Anales 2011, Instituto de Actuarios Españoles, 51-74.
• Smyth G. K., Jørgensen B. (2002) Fitting Tweedie's compound Poisson model to insurance claims data: dispersion modelling, ASTIN Bulletin 32(1), 143-157.
• Taylor G. C. (2000) Claim Reserving. An Actuarial Perspective, Elsevier Science Publishers, New York.
• Wüthrich M. V. (2003) Claims reserving using Tweedie's compound Poisson model, ASTIN Bulletin 33(2), 331-346.
• Wüthrich M. V., Merz M. (2008) Stochastic claims reserving methods in insurance, Wiley.
• Wüthrich M. V., Merz M., Lysenko N. (2009) Uncertainty in the claims development result in the chain ladder method, Scand. Actuar. J. 109(1), 63-84.
• Zieliński R. (1983) Robust statistical procedures: a general approach, Lecture Notes in Mathematics 982, Springer-Verlag, 283-295.