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A stochastic model for time lag in reporting of claims

Published online by Cambridge University Press:  14 July 2016

Jan-Erik Karlsson
Jan-Erik Karlsson*
Affiliation:
University of Stockholm
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Abstract

We assume that the number of claims occur according to a renewal process and treat the number of claims that occur and are reported in a certain time interval as a renewal process with random displacements. We obtain a renewal equation for the mean value function and an integral equation for the Laplace transform of the distribution of the claims that are reported. We also give asymptotic expressions for the mean value function and calculate the generating function in the case where the renewal process is a Poisson process. This matter is a part of the IBNR-problem in insurance mathematics.

Keywords

INCURRED BUT NOT REPORTED CLAIMSRENEWAL PROCESS WITH RANDOM DISPLACEMENTS
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 382 - 387
Copyright
Copyright © Applied Probability Trust 1974 

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References

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