An optimal dividends problem with transaction costs for spectrally negative Lévy processes. (English) Zbl 1231.91211

Summary: We consider an optimal dividends problem with transaction costs where the reserves are modeled by a spectrally negative Lévy process. We make the connection with the classical de Finetti problem and show in particular that when the Lévy measure has a log-convex density, then an optimal strategy is given by paying out a dividend in such a way that the reserves are reduced to a certain level \(c_{1}\) whenever they are above another level \(c_{2}\). Further we describe a method to numerically find the optimal values of \(c_{1}\) and \(c_{2}\).


91B30 Risk theory, insurance (MSC2010)
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