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Distributional study of De Finetti’s dividend problem for a general Lévy insurance risk process. (English) Zbl 1137.60047
The authors provide a study of the solution to the classical control problem, which concerns the optimal payment of dividends from an insurance risk process prior to ruin. They build on recent work in the actuarial literature concerning calculations of the \(n\)-th moment of the net present value of dividends paid out in the optimal strategy as well as the moments of the deficit at ruin and the Laplace transform of the red period. The calculations presented in the article are valid for a general spectrally negative Lévy process as opposed to the classical Cramer-Lundberg process with exponentially distributed jumps.

60K10 Applications of renewal theory (reliability, demand theory, etc.)
91B30 Risk theory, insurance (MSC2010)
60K05 Renewal theory
60K15 Markov renewal processes, semi-Markov processes
60G51 Processes with independent increments; Lévy processes
60G70 Extreme value theory; extremal stochastic processes
60J55 Local time and additive functionals
Full Text: DOI
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