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On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes. (English) Zbl 1152.60344
Summary: We consider the classical optimal dividend control problem which was proposed by B. de Finetti [Trans. XVth Internat. Congress Actuaries 2, 433–443 (1957)]. Recently F. Avram, Z. Palmowski and M. R. Pistorius [Ann. Appl. Probab. 17, No. 1, 156–180 (2007; Zbl 1136.60032)] studied the case when the risk process is modeled by a general spectrally negative Lévy process. We draw upon their results and give sufficient conditions under which the optimal strategy is of barrier type, thereby helping to explain the fact that this particular strategy is not optimal in general. As a consequence, we are able to extend considerably the class of processes for which the barrier strategy proves to be optimal.

MSC:
60J99 Markov processes
93E20 Optimal stochastic control
60G51 Processes with independent increments; Lévy processes
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