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Predicting Ibnyr Events and Delays: I. Continuous Time

Published online by Cambridge University Press:  29 August 2014

William S. Jewell
William S. Jewell*
Affiliation:
Engineering Systems Research Center, University of California, Berkely
*
Engineering Systems Research Center, University of California, Berkeley, CA 94720.
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Abstract

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An IBNYR event is one that occurs randomly during some fixed exposure interval and incurs a random delay before it is reported. Both the rate at which such events occur and the parameters of the delay distribution are unknown random quantities. Given the number of events that have been reported during some observation interval, plus various secondary data on the dates of the events, the problem is to estimate the true values of the unknown parameters and to predict the number of events that are still unreported. A full-distributional Bayesian model is used, and it is shown that the amount of secondary data is critical. A recursive procedure calculates the predictive density; however, an explicit formula for the predictive mode can be obtained. The main computational work is the evaluation of an integral involving the prior density of the delay parameters, but this can be simplified in the exponential case using Gammoid approximations.

Keywords

Observations delaysInccurred But Not Reported (IBNR) modelsBayesian estimation and prediction
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 19 , Issue 1 , April 1989 , pp. 25 - 55
Copyright
Copyright © International Actuarial Association 1989

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