×

Accounting year effects modeling in the stochastic chain ladder reserving method. (English) Zbl 1219.91074

Summary: In almost all stochastic claims reserving models one assumes that accident years are independent. In practice this assumption is violated most of the time. Typical examples are claims inflation and accounting year effects that influence all accident years simultaneously. We study a Bayesian chain ladder model that allows for accounting (calendar) year effects modeling. A case study of a general liability dataset shows that such accounting year effects contribute substantially to the prediction uncertainty and therefore need a careful treatment within a risk management and solvency framework.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics

Software:

BUGS
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Alba de E., North American Actuarial Journal 6 (4) pp 1– (2002) · Zbl 1084.62554
[2] Alba de E., North American Actuarial Journal 10 (3) pp 45– (2006)
[3] Alba de E., Insurance: Mathematics and Economics 43 pp 368– (2008) · Zbl 1152.91719
[4] Asmussen S., Stochastic Simulation (2007)
[5] Barnett G., Proceedings of the CAS 87 pp 245– (2000)
[6] Bühlmann H., Astin Bulletin 39 (1) pp 275– (2009) · Zbl 1205.91078
[7] Bühlmann H., A Course in Credibility Theory and Its Applications (2005) · Zbl 1108.91001
[8] Clark D. R., CAS Forum pp 61– (2006)
[9] D’Arcy S. P., CAS E-Forum pp 98– (2008)
[10] England P. D., Annals of Actuarial Science 1 (2) pp 221– (2006)
[11] Gilks W. R., Markov Chain Monte Carlo in Practice (1996) · Zbl 0832.00018
[12] Gisler A., ASTIN Bulletin 38 (2) pp 565– (2008) · Zbl 1274.91486
[13] Hastings W. K., Biometrika 57 pp 97– (1970) · Zbl 0219.65008
[14] Hertig J., Astin Bulletin 15 (2) pp 171– (1985)
[15] Jong, de P., North American Actuarial Journal 10 (2) pp 28– (2006)
[16] Mack T., ASTIN Bulletin 23 (2) pp 213– (1993)
[17] Metropolis N., Journal of Chemistry and Physics 21 (6) pp 1087– (1953)
[18] Murphy D. M., Proceedings of the CAS 81 pp 154– (1994)
[19] Ntzoufras I., North American Actuarial Journal 6 (1) pp 113– (2002) · Zbl 1084.62544
[20] Peters G. W., ASTIN Bulletin 39 (1) pp 1– (2009) · Zbl 1203.91114
[21] Roberts G. O., Annals of Applied Probability 7 pp 110– (1997) · Zbl 0876.60015
[22] Sandström A., Solvency: Models, Assessment and Regulation (2006) · Zbl 1124.91041
[23] Scollnik D. P. M., North American Actuarial Journal 5 (2) pp 96– (2001) · Zbl 1083.62543
[24] Spiegelhalter D. J., Journal of the Royal Statistical Society 64 pp 583– (2002) · Zbl 1067.62010
[25] Spiegelhalter D. J., BUGS: Bayesian Inference Using Gibbs Sampling, Version 0.5 (1995)
[26] Verrall R. J., North American Actuarial Journal 8 (3) pp 67– (2004) · Zbl 1085.62516
[27] Wuthrigh M. V., Insurance: Mathematics and Economics 42 (1) pp 378– (2008) · Zbl 1141.91644
[28] Wuthrigh M. V., Stochastic Claims Reserving Methods in Insurance (2008)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.