On the time to ruin and the deficit at ruin in a risk model with double-sided jumps. (English) Zbl 1153.91024

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.


91B30 Risk theory, insurance (MSC2010)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
60J65 Brownian motion
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