A two-dimensional ruin problem on the positive quadrant, with exponential claims: Feynman- Kac formula, Laplace transform and its inversion

• Autores: Florin Avram, Z. Palmowski, M. Pistorius
• Localización: Ninth international conference Zaragoza-Pau on applied mathematics and statistics: Jaca (Spain). September 19-21, 2005 / coord. por Monique Madaune-Tort, 2006, ISBN 84-7733-871-X, págs. 199-206
• Idioma: inglés
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• Resumen

  • We consider an exit problem of a certain two-dimensional process from a cone, inspired by applications in insurance and queueing theory. One motivation is to study the joint ruin problem for two insurance companies (insurance/reinsurance), or for two branches of the same company, which divide between them both claims and premia in some specified proportions, the goal being to split the risk (in particular when the claims are big). Another motivation is to provide an example of a multi-dimensional ruin model admitting analytic solutions. Indeed, we succeed, in the simplest particular case of exponential claims, to derive both the Laplace transform of the perpetual ruin probabilities, and to invert it, obtaining therefore an explicit solution for our model