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Zbl 1153.91024
Xing, Xiaoyu; Zhang, Wei; Jiang, Yiming
On the time to ruin and the deficit at ruin in a risk model with double-sided jumps. (English)
[J] Stat. Probab. Lett. 78, No. 16, 2692-2699 (2008). ISSN 0167-7152

Summary: We consider a jump diffusion risk model, which consists of a Brownian motion, phase type distributed positive claims and general negative claims. The distributions of the time to ruin and the deficit at ruin will be studied by using Rouché's Theorem, martingale and matrix analysis. We derive an explicit joint Laplace transform for the time to ruin and the deficit at ruin, as well as the Laplace transform for the time to ruin. Furthermore, our results still hold even when positive claims are rationally distributed.

MSC 2000:: *91B30 Risk theory etc.
60J70 Appl. of diffusion theory
60J65 Brownian motion

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