Skip to main content Accessibility help
×
Home

EXISTENCE AND UNIQUENESS OF CHAIN LADDER SOLUTIONS

  • Greg Taylor (a1)

Abstract

The cross-classified chain ladder has a number of versions, depending on the distribution to which observations are subject. The simplest case is that of Poisson distributed observations, and then maximum likelihood estimates of parameters are explicit. Most other cases, however, including Bayesian chain ladder models, lead to implicit MAP (Bayesian) or MLE (non-Bayesian) solutions for these parameter estimates, raising questions as to their existence and uniqueness. The present paper investigates these questions in the case where observations are distributed according to some member of the exponential dispersion family.

Copyright

References

Hide All
England, P.D. and Verrall, R.J. (2002) Stochastic claims reserving in general insurance. British Actuarial Journal, 8 (iii), 443518.
England, P.D., Verrall, R.J. and Wüthrich, M.V. (2012) Bayesian over-dispersed Poisson model and the Bornhuetter & Ferguson claims reserving method. Annals of Actuarial Science, 6 (2), 258281.
Gisler, A. and Müller, P. (2007) Credibility for additive and multiplicative models. Paper presented to the 37th ASTIN Colloquium, Orlando FL, USA. See http://www.actuaries.org/ASTIN/Colloquia/Orlando/Presentations/Gisler2.pdf.
Gisler, A. and Wüthrich, M.V. (2008) Credibility for the chain ladder reserving method. Astin Bulletin, 38 (2), 565597.
Hachemeister, C. A. and Stanard, J.N. (1975) IBNR claims count estimation with static lag functions. Spring meeting of the Casualty Actuarial Society.
Kuang, D., Nielsen, B. and Nielsen, J.P. (2008) Identification of the age-period-cohort model and the extended chain ladder model. Biometrika, 95, 979986.
Kuang, D., Nielsen, B. and Nielsen, J.P. (2009) Chain-ladder as maximum likelihood revisited. Annals of Actuarial Science, 4 (1), 105121.
Mack, T. (1993) Distribution-free calculation of the standard error of chain ladder reserve estimates. Astin Bulletin, 23 (2), 213225.
McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models, 2nd ed. London, UK: Chapman & Hall.
Merz, M., Wüthrich, M.V. and Hashorva, E. (2013) Dependence modelling in multivariate claims run-off triangles. Annals of Actuarial Science, 7 (1), 325.
Renshaw, A.E. and Verrall, R.J. (1998) A stochastic model underlying the chain-ladder technique. British Actuarial Journal, 4 (iv), 903923.
Shi, P., Basu, S. and Meyers, P.P. (2012) A Bayesian log-normal model for multivariate loss reserving. North American Actuarial Journal, 16 (1), 2951.
Taylor, G. (2000) Loss Reserving: An Actuarial Perspective. Boston: Kluwer Academic Publishers.
Taylor, G. (2009) The chain ladder and Tweedie distributed claims data. Variance, 3, 96104.
Taylor, G. (2011) Maximum likelihood and estimation efficiency of the chain ladder. Astin Bulletin, 41 (1), 131155.
Taylor, G. (2015) Bayesian chain ladder models. Astin Bulletin, 45 (1), 7599.
Tweedie, M. C. K. (1984) An index which distinguishes between some important exponential families. In Statistics: Applications and New Directions, Proceedings of the Indian Statistical Golden Jubilee International Conference (ed. Ghosh, J.K. and Roy, J.), pp. 579604. Indian Statistical Institute.
Verrall, R.J. (2000) An investigation into stochastic claims reserving models and the chain-ladder technique. Insurance: Mathematics and Economics, 26 (1), 9199.
Verrall, R.J. (2004) A Bayesian generalised linear model for the Bornhuetter-Ferguson method of claims reserving. North American Actuarial Journal, 8 (3), 6789.
Wüthrich, M.V. (2003) Wüthrich M V (2007). Claims reserving using Tweedie's compound Poisson model. Astin Bulletin, 33 (2), 331346.
Wüthrich, M.V. (2007) Using a Bayesian approach for claims reserving. Variance, 1 (2), 292301.
Wüthrich, M.V. (2012) Discussion of “A Bayesian log-normal model for multivariate loss reserving” by Shi-Basu-Meyers. North American Actuarial Journal, 16 (3), 398401.
Wüthrich, M.V. and Merz, M. (2008). Stochastic Claims Reserving Methods in Insurance, Chichester, UK: John Wiley & Sons Ltd.

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed