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

Abstract

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 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.

arXiv commentPublished in at http://dx.doi.org/10.1214/07-AAP504 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• On the optimal dividend problem for a spectrally negative Lévy process
• Ruin probabilities and decompositions for general perturbed risk processes
• Smoothness of scale functions for spectrally negative Levy processes

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