The Annals of Applied Probability

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

R. L. Loeffen

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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.

Article information

Source
Ann. Appl. Probab. Volume 18, Number 5 (2008), 1669-1680.

Dates
First available in Project Euclid: 30 October 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1225372945

Digital Object Identifier
doi:10.1214/07-AAP504

Mathematical Reviews number (MathSciNet)
MR2462544

Zentralblatt MATH identifier
1152.60344

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

Keywords
Lévy process stochastic control dividend problem scale function complete monotonicity

Citation

Loeffen, R. L. On optimality of the barrier strategy in de Finetti’s dividend problem for spectrally negative Lévy processes. Ann. Appl. Probab. 18 (2008), no. 5, 1669--1680. doi:10.1214/07-AAP504. https://projecteuclid.org/euclid.aoap/1225372945.


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