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A Risk Model with Delayed Claims

Part of: Limit theorems Stochastic processes Mathematical economics

Published online by Cambridge University Press:  30 January 2018

Angelos Dassios  and
Hongbiao Zhao
Angelos Dassios*
Affiliation:
London School of Economics
Hongbiao Zhao*
Affiliation:
London School of Economics
*
∗ Postal address: Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK.
∗ Postal address: Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK.
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Abstract

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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.

Keywords

Delayed claimrisk modelruin probabilityasymptoticsgeneralised Cramér‒Lundberg approximationnonhomogeneous Poisson process

MSC classification

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

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 3 , September 2013 , pp. 686 - 702
Copyright
© Applied Probability Trust 

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