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The compound Poisson risk model with multiple thresholds. (English) Zbl 1152.91592
Summary: We consider a multi-threshold compound Poisson risk model. A piecewise integro-differential equation is derived for the Gerber-Shiu discounted penalty function. We then provide a recursive approach to obtain general solutions to the integro-differential equation and its generalizations. Finally, we use the probability of ruin to illustrate the applicability of the approach.

MSC:
91B30 Risk theory, insurance (MSC2010)
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