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On optimal periodic dividend and capital injection strategies for general Lévy models (2505.06554v1)
Published 10 May 2025 in math.PR and math.OC
Abstract: We consider a version of de Finetti's dividend problem, with the bail-out contraint to keep the surplus non-negative, and where dividend payments can only be made at the arrival times of an independent Poisson process. For a general L\'evy process with positive and negative jumps, we show the optimality of a periodic-classical reflection strategy that pays the excess above a given level at each Poisson arrival time, and also reflects below at 0 in the classical sense.