Ruin time and aggregate claim amount up to ruin time for the perturbed risk process |
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Authors: | Landy Rabehasaina Cary Chi-Liang Tsai |
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Institution: | 1. Laboratoire de Mathématiques , Université de Franche-Comté , Besan?on cédex , France lrabehas@univ-fcomte.fr;3. Department of Statistics &4. Actuarial Science , Simon Fraser University , Burnaby , BC , Canada |
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Abstract: | We consider the classical Sparre-Andersen risk process perturbed by a Wiener process, and study the joint distribution of the ruin time and the aggregate claim amounts until ruin by determining its Laplace transform. This is first done when the claim amounts follow respectively an exponential/Phase-type distribution, in which case we also compute the distribution of recovery time and study the case of a barrier dividend. Then the general distribution is considered when ruin occurs by oscillation, in which case a renewal equation is derived. |
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Keywords: | Sparre-Andersen risk process Laplace transform Brownian motion Markov modulated first time passage process risk theory |
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