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A Two-Dimensional Risk Model with Proportional Reinsurance

Part of: Markov processes Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Andrei L. Badescu ,
Eric C. K. Cheung  and
Landy Rabehasaina
Andrei L. Badescu*
Affiliation:
University of Toronto
Eric C. K. Cheung*
Affiliation:
University of Hong Kong
Landy Rabehasaina*
Affiliation:
Université de Franche Comté
*
∗ Postal address: Department of Statistics, University of Toronto, 100 St. George Street, Toronto, Ontario, Canada. Email address: badescu@utstat.toronto.edu
∗∗ Postal address: Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam, Hong Kong. Email address: eckc@hku.hk
∗∗∗ Postal address: Département de Mathématiques, Université de Franche Comté, 16 route de Gray, 25030 Besançon, France. Email address: lrabehas@univ-fcomte.fr
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Abstract

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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.

Keywords

Two-dimensional risk modelproportional reinsurancegeometric argumentabsorbing settime to ruindeficit at ruin

MSC classification

Secondary: 60G51: Processes with independent increments; L'evy processes 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60J75: Jump processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 749 - 765
Copyright
Copyright © Applied Probability Trust 2011 

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