A two-dimensional ruin problem on the positive quadrant
AbstractIn 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 Cramér-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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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 42 (2008)
Issue (Month): 1 (February)
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Web page: http://www.elsevier.com/locate/inca/505554
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- Irmina Czarna & Zbigniew Palmowski, 2009. "De Finetti's dividend problem and impulse control for a two-dimensional insurance risk process," Papers 0906.2100, arXiv.org, revised Feb 2011.
- Macci, Claudio, 2011. "Large deviations for estimators of unknown probabilities, with applications in risk theory," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 16-24, January.
- Debicki, K. & Kosinski, K.M. & Mandjes, M. & Rolski, T., 2010. "Extremes of multidimensional Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2289-2301, December.
- Bäuerle, Nicole & Blatter, Anja, 2011. "Optimal control and dependence modeling of insurance portfolios with Lévy dynamics," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 398-405, May.
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