## Journal of Applied Probability

- J. Appl. Probab.
- Volume 48, Number 3 (2011), 749-765.

### A two-dimensional risk model with proportional reinsurance

Andrei L. Badescu, Eric C. K. Cheung, and Landy Rabehasaina

#### Abstract

In this paper we consider an extension of the two-dimensional risk model introduced in Avram, Palmowski and Pistorius (2008a). To this end, we assume that there are two insurers. The first insurer is subject to claims arising from two independent compound Poisson processes. The second insurer, which can be viewed as a different line of business of the same insurer or as a reinsurer, covers a proportion of the claims arising from one of these two compound Poisson processes. We derive the Laplace transform of the time until ruin of at least one insurer when the claim sizes follow a general distribution. The surplus level of the first insurer when the second insurer is ruined first is discussed at the end in connection with some open problems.

#### Article information

**Source**

J. Appl. Probab., Volume 48, Number 3 (2011), 749-765.

**Dates**

First available in Project Euclid: 23 September 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.jap/1316796912

**Digital Object Identifier**

doi:10.1239/jap/1316796912

**Mathematical Reviews number (MathSciNet)**

MR2884813

**Zentralblatt MATH identifier**

1239.91073

**Subjects**

Primary: 60G51: Processes with independent increments; Lévy processes

Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 60J75: Jump processes

**Keywords**

Two-dimensional risk model proportional reinsurance geometric argument absorbing set time to ruin deficit at ruin

#### Citation

Badescu, Andrei L.; Cheung, Eric C. K.; Rabehasaina, Landy. A two-dimensional risk model with proportional reinsurance. J. Appl. Probab. 48 (2011), no. 3, 749--765. doi:10.1239/jap/1316796912. https://projecteuclid.org/euclid.jap/1316796912