Journal of Applied Probability

An optimal dividends problem with a terminal value for spectrally negative Lévy processes with a completely monotone jump density

R. L. Loeffen

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We consider a modified version of the classical optimal dividends problem of de Finetti in which the objective function is altered by adding in an extra term which takes account of the ruin time of the risk process, the latter being modeled by a spectrally negative Lévy process. We show that, with the exception of a small class, a barrier strategy forms an optimal strategy under the condition that the Lévy measure has a completely monotone density. As a prerequisite for the proof, we show that, under the aforementioned condition on the Lévy measure, the q-scale function of the spectrally negative Lévy process has a derivative which is strictly log-convex.

Article information

J. Appl. Probab. Volume 46, Number 1 (2009), 85-98.

First available in Project Euclid: 1 April 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J99: None of the above, but in this section
Secondary: 93E20: Optimal stochastic control 60G51: Processes with independent increments; Lévy processes

Lévy process stochastic control dividend problem scale function complete monotonicity


Loeffen, R. L. An optimal dividends problem with a terminal value for spectrally negative Lévy processes with a completely monotone jump density. J. Appl. Probab. 46 (2009), no. 1, 85--98. doi:10.1239/jap/1238592118.

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