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Perturbed MAP risk models with dividend barrier strategies. (English) Zbl 1180.60071
The authors consider surplus processes for which the claim number process is a Markov two dimensional arrival process (MAP) for which the first dimension represents the evolution of the total number of claims and the second one refers to the evolution of an underlying homogeneous continuous – time Markov chain (CTMC). “Such machinery is used to analyze the moments of the discounted dividend payments and the expected discounted penalty. The authors prove, that a dividend-penalty identity type relationship holds for the class of perturbed MAPs. All the ruin – related quantities are revisited in an identical MAP risk model subject to a dividend barrier strategy for which the barrier level effective at given time depends on the state of the CTMC at that time. A numerical example shows the impact of a barrier level on the expected discounted dividend payment and illustrates the proposed methodology.

MSC:
60J75 Jump processes (MSC2010)
60J25 Continuous-time Markov processes on general state spaces
60J60 Diffusion processes
91B30 Risk theory, insurance (MSC2010)
91B70 Stochastic models in economics
60J27 Continuous-time Markov processes on discrete state spaces
91B26 Auctions, bargaining, bidding and selling, and other market models
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