## Journal of Applied Probability

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

### A risk model with delayed claims

Angelos Dassios and Hongbiao Zhao

#### 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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 5 September 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1378401230

**Digital Object Identifier**

doi:10.1239/jap/1378401230

**Mathematical Reviews number (MathSciNet)**

MR3102509

**Zentralblatt MATH identifier**

1278.91084

**Subjects**

Primary: 91B30: Risk theory, insurance

Secondary: 60G55: Point processes 60F05: Central limit and other weak theorems

**Keywords**

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

#### Citation

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