On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes

Details On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes On optimality of the barrier strategy in de Finetti's dividend problem for spectrally negative Lévy processes

2008-11-12

arxiv.org/abs/0811.1862v1

Annals of Applied Probability 2008, Vol. 18, No. 5, 1669-1680

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AAP504 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/07-AAP504

We consider the classical optimal dividend control problem which was proposed by de Finetti [Trans. XVth Internat. Congress Actuaries 2 (1957) 433--443]. Recently Avram, Palmowski and Pistorius [Ann. Appl. Probab. 17 (2007) 156--180] studied the case when the risk process is modeled by a general spectrally negative L\'{e}vy 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.

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