A two-dimensional ruin problem on the positive quadrant

Details A two-dimensional ruin problem on the positive quadrant A two-dimensional ruin problem on the positive quadrant

2007-11-15

arxiv.org/abs/0711.2465v1

Mathematics

Probability

2 figures, 19pp

Scientific paper

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cram\'{e}r-Lundberg processes we obtain the Laplace transform in space of the probability that either of the insurance companies is ruined in finite time. Subsequently, for exponentially distributed claims, we derive an explicit analytical expression for this joint ruin probability by explicitly inverting this Laplace transform. We also provide a characterization of the Laplace transform of the joint ruin time.

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