A Risk Model with Delayed Claims. (30th January 2018)

• Record Type: Journal Article
• Authors: Dassios, Angelos; Zhao, Hongbiao
• Is Part Of: Journal of applied probability. Volume 50:Number 3(2013)
• Page Start: 686
• Page End: 702
• Publication Date: 2018-01-30
• Subjects: Delayed claim, -- risk model, -- ruin probability, -- asymptotics, -- generalised Cramér‒Lundberg approximation, -- nonhomogeneous Poisson process; 91B30, -- 60G55, -- 60F05; 519.2
• DOI: 10.1239/jap/1378401230
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : 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.