A Risk Model with Delayed Claims
19 Pages Posted: 9 Feb 2015
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
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