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On optimality of the barrier strategy for a general Lévy risk process. (English) Zbl 1219.91076

Summary: We consider the optimal dividend problem for the insurance risk process in a general Lévy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give sufficient conditions under which the optimal strategy is of barrier type. In particular, we show that if the Lévy density is a completely monotone function, then the optimal dividend strategy is a barrier strategy. This approach was inspired by the work of F. Avram, Z. Palmowski and M. R. Pistorius [Ann. Appl. Probab. 17, No. 1, 156–180 (2007; Zbl 1136.60032)], R. L. Loeffen [Ann. Appl. Probab. 18, No. 5, 1669–1680 (2008; Zbl 1152.60344)] and A. E. Kyprianou, V. Rivero and R. Song [J. Theor. Probab. 23, No. 2, 547–564 (2010; Zbl 1188.93115)] in which the same problem was considered under the spectrally negative Lévy processes setting.

MSC:

91B30 Risk theory, insurance (MSC2010)
60G51 Processes with independent increments; Lévy processes
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References:

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