A Risk Model with Delayed Claims

19 Pages Posted: 9 Feb 2015

See all articles by Angelos Dassios

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics

Hongbiao Zhao

Shanghai University of Finance and Economics; London School of Economics & Political Science (LSE)

Date Written: June 10, 2013

Abstract

In this paper, we introduce a simple risk model with delayed claims, an extension of the classical Poisson model. The arrival of claims is assumed to be a Poisson process, 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 when the claims are also exponentially distributed.

Keywords: Delayed claims, Risk model, Ruin probability, Asymptotics, Generalised Cramer-Lundberg approximation, Non-homogeneous Poisson process

JEL Classification: C10

Suggested Citation

Dassios, Angelos and Zhao, Hongbiao, A Risk Model with Delayed Claims (June 10, 2013). Journal of Applied Probability, Vol. 50, No. 3, 2013, Available at SSRN: https://ssrn.com/abstract=2561968

Angelos Dassios

London School of Economics & Political Science (LSE) - Department of Statistics ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

Hongbiao Zhao (Contact Author)

Shanghai University of Finance and Economics ( email )

No. 777 Guoding Road
Yangpu District
Shanghai, Shanghai 200433
China

HOME PAGE: http://hongbiaozhao.weebly.com/

London School of Economics & Political Science (LSE)

Houghton Street
London, WC2A 2AE
United Kingdom

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