Journal of Applied Probability

A risk model with delayed claims

Angelos Dassios and Hongbiao Zhao

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In this paper we introduce a simple risk model with delayed claims, an extension of the classical Poisson model. The claims are assumed to arrive according to a Poisson process and claims follow a light-tailed distribution, and each loss payment of the claims will be settled with a random period of delay. We obtain asymptotic expressions for the ruin probability by exploiting a connection to Poisson models that are not time homogeneous. A finer asymptotic formula is obtained for the special case of exponentially delayed claims and an exact formula is obtained when the claims are also exponentially distributed.

Article information

J. Appl. Probab., Volume 50, Number 3 (2013), 686-702.

First available in Project Euclid: 5 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 91B30: Risk theory, insurance
Secondary: 60G55: Point processes 60F05: Central limit and other weak theorems

Delayed claim risk model ruin probability asymptotics generalised Cramér‒Lundberg approximation nonhomogeneous Poisson process


Dassios, Angelos; Zhao, Hongbiao. A risk model with delayed claims. J. Appl. Probab. 50 (2013), no. 3, 686--702. doi:10.1239/jap/1378401230.

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