Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-12T00:10:02.411Z Has data issue: false hasContentIssue false
  • English
  • Français

Predicting IBNYR Events and Delays II. Discrete Time

Published online by Cambridge University Press:  29 August 2014

William S. Jewell
William S. Jewell*
Affiliation:
Engineering Systems Research Center, University of Californiaat Berkeley
*
Department of Industrial Engineering & Operations Research, 4173 Etcheverry Hall, University of California, Berkeley, California 94720, USA.
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.

An IBNYR event is one that occurs randomly during some fixed exposure interval and incurs a random delay before it is reported. A previous paper developed a continuous-time model of the IBNYR process in which both the Poisson rate at which events occur and the parameters of the delay distribution are unknown random quantities; a full-distributional Bayesian method was then developed to predict the number of unreported events. Using a numerical example, the success of this approach was shown to depend upon whether or not the occurrence dates were available in addition to the reporting dates. This paper considers the more usual practical situation in which only discretized epoch information is available; this leads to a loss of predictive accuracy, which is investigated by considering various levels of quantization for the same numerical example.

Keywords

Incurred But Not Reported (IBNR) modelsreporting delaysBayesian estimation and predictionBayesian approximationsdiscrete-time models
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 20 , Issue 1 , April 1990 , pp. 93 - 111
Copyright
Copyright © International Actuarial Association 1990

References

PARTIAL REFERENCES

Jewell, W. S. (1989) Predicting IBNYR events and delays. ASTIN Bulletin 19, 25–55.CrossRefGoogle Scholar
Kass, R. E., Tierney, L. and Kadane, J.B. (1988) Asymptotics in Bayesian computation. In Bayesian Statistics 3, Bernardo, J. M., DeGroot, M. H. and Smith, A. F. M. (Eds.), Oxford University Press, 261–278.Google Scholar
Kahane, Y. (1989) A modern approach to loss reserving in long-tail lines — the case of automobile insurance. Transactions, XXIth ASTIN Colloquium, New York, 175–197.Google Scholar
Reinsurance Association of America (1987) Loss development study. Transactions, XXIth ASTIN Colloquium, New York, 525–583.Google Scholar
Schnieper, R. (1989) A pragmatic IBNR method. Transactions, XXIth ASTIN Colloquium, New York, 405–425.Google Scholar
Stiers, D. (1989) Applications de méthodes d'évaluation des réserves. Transactions, XXIth ASTIN Colloquium, New York, 441–463.Google Scholar
Tierney, L. and Kadane, J.B. (1986) Accurate approximations for posterior moments and marginal densities. J. Amer. Statist. Assoc. 81, 82–86.CrossRefGoogle Scholar
Weller, A.O. (1989) Generalized Bondy development. Transactions, XXIth ASTIN Colloquium, New York, 585–609.Google Scholar