Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T05:03:08.951Z Has data issue: false hasContentIssue false
  • English
  • Français

Modelling of Discretized Claim Numbers in Loss Reserving

Published online by Cambridge University Press:  29 August 2014

Ole Hesselager
Ole Hesselager*
Affiliation:
University of Copenhagen, Laboratory of Actuarial Mathematics
*
University of Copenhagen, Laboratory of Actuarial Mathematics, Universitetsparken 5, DK-2J00 Copenhagen Ø, Denmark
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the usual method of discretizing loss reserving data by calendar year and show how this procedure may introduce fluctuations in the delay probabilities. These fluctuations, when treated as random fluctuations, possess a special correlation structure and we present a simple credibility method accounting for these fluctuations. The results are illustrated by a numerical example.

Keywords

Loss reservingClaim numbersPoisson processDiscretizing by calendar yearVariations in delay probabilitiesCredibility adjustments
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 25 , Issue 2 , November 1995 , pp. 119 - 135
Copyright
Copyright © International Actuarial Association 1995

References

Beard, R.E., Pentikäinen, T. and Pesonen, E. (1984) Risk Theory. 3rd edition. Chapman and Hall, London.CrossRefGoogle Scholar
Benktander, G. and Segerdahl, C.O. (1960) On the analytical representation of claim distributions with special reference to excess of loss reinsurance. Transactions of the International Congress of Actuaries.Google Scholar
Ferguson, T.S. (1973) A Bayesian analysis of some nonparametric problems. The Annals of Statistics, 1, 209–230.CrossRefGoogle Scholar
Hess, K.T. and Schmidt, K.D. (1994a) A remark on modelling IBNR claim numbers with random delay pattern. Technical report. Dresdner Schriften zur Versicherungsmathematik, 4/1994.Google Scholar
Hess, K.T. and Schmidt, K.D. (1994b) Experience reserving under vague prior information. Technical report. Dresdner Schriften zur Versicherungsmathematik, 5/1994.Google Scholar
Hesselager, O. and Witting, T. (1988) A credibility model with random fluctuations in delay probabilities for the prediction of IBNR claims. ASTIN Bulletin, 18, 79–90.CrossRefGoogle Scholar
Hogg, R. V. and Klugman, S.A. (1984) Loss Distributions. Wiley, New York.CrossRefGoogle Scholar
Kaas, R., Van Heerwaarden, A. and Goovaerts, M.J. (1994) Ordering of Actuarial Risks. Caire Education Series I, Ceuterick.Google Scholar
Lawless, J.F. (1994) Adjustments for reporting delays and the prediction of occurred but not reported events. Canadian Journ. Stat., 22, 15–31.CrossRefGoogle Scholar
Neuhaus, W. (1992) IBNR models with random delay distributions. Scand. Actuarial J., 1992, 97–107.CrossRefGoogle Scholar
Norberg, R. (1986) A contribution to modelling of IBNR claims. Scand. Actuarial J., 1986, 155–203.CrossRefGoogle Scholar
Norberg, R. (1993) Prediction of outstanding liabilities in non-life insurance. ASTIN Bulletin, 23, 95–115.CrossRefGoogle Scholar
Sundt, B. (1984) An Introduction to Non-life Insurance Mathematics. 28, 1st edition. Verlag Versicherungswirtschaft, Karlsruhe.Google Scholar
Sundt, B. (1993) An Introduction to Non-life Insurance Mathematics. 28, 3rd edition. Verlag Versicherungswirtschaft, Karlsruhe.Google Scholar
Van Heerwaarden, A. (1991) Ordering of Risks. Ph.D. thesis, University of Amsterdam, 1991.Google Scholar