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On the expected discounted penalty function in a delayed-claims risk model. (English) Zbl 1355.60111

Summary: In this paper, we consider a risk model in which each main claim may induce a delayed claim, called a by-claim. We assume that the time for the occurrence of a by-claim is random. We investigate the expected discounted penalty function, and derive the defective renewal equation satisfied by it. We obtain some explicit results when the main claim and the by-claim are both exponentially distributed, respectively. We also present some numerical illustrations.

MSC:

60J65 Brownian motion
62P05 Applications of statistics to actuarial sciences and financial mathematics
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