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Dividend problem with Parisian delay for a spectrally negative Lévy risk process. (English) Zbl 1296.91150
The authors consider a spectrally negative Lévy risk process modelling the surplus of an insurance company. This process is controlled by a dividend policy \(\pi\). The so-called barrier strategy is applied: the decision to pay dividend is taken when the surplus reaches a fixed barrier. The objective is to maximize the average cumulative discounted dividends received until the moment of ruin. Two possibilities of a Parisian delay are considered. The first one is the delay between the decision to pay and its implementation. The dividend is paid only if the surplus stays above the barrier longer than a fixed amount of time. The second type of delay is the Parisian delay at the ruin. Ruin occurs if the surplus stays below zero longer than a fixed period of time.

MSC:
91B30 Risk theory, insurance (MSC2010)
60G51 Processes with independent increments; Lévy processes
60H30 Applications of stochastic analysis (to PDEs, etc.)
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