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Weak convergence approach to compound Poisson risk processes perturbed by diffusion. (English) Zbl 1242.91097

Summary: We obtain the ruin probability and expected discounted penalty function for a diffusion-perturbed classical risk model, by taking limits in a sequence of compound Poisson processes that converge weakly to the former. This allows us to improve upon a result of C. C. L. Tsai and G. E. Willmot [Insur. Math. Econ. 30, No. 1, 51–66 (2002; Zbl 1074.91563)].

MSC:

91B30 Risk theory, insurance (MSC2010)
60F05 Central limit and other weak theorems
60J60 Diffusion processes
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)

Citations:

Zbl 1074.91563
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References:

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