The Annals of Applied Probability

On the optimal dividend problem for a spectrally negative Lévy process

Florin Avram, Zbigniew Palmowski, and Martijn R. Pistorius

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Abstract

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative Lévy process in the absence of dividend payments. The classical dividend problem for an insurance company consists in finding a dividend payment policy that maximizes the total expected discounted dividends. Related is the problem where we impose the restriction that ruin be prevented: the beneficiaries of the dividends must then keep the insurance company solvent by bail-out loans. Drawing on the fluctuation theory of spectrally negative Lévy processes we give an explicit analytical description of the optimal strategy in the set of barrier strategies and the corresponding value function, for either of the problems. Subsequently we investigate when the dividend policy that is optimal among all admissible ones takes the form of a barrier strategy.

Article information

Source
Ann. Appl. Probab. Volume 17, Number 1 (2007), 156-180.

Dates
First available in Project Euclid: 13 February 2007

Permanent link to this document
http://projecteuclid.org/euclid.aoap/1171377180

Digital Object Identifier
doi:10.1214/105051606000000709

Mathematical Reviews number (MathSciNet)
MR2292583

Zentralblatt MATH identifier

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 dividend problem local time reflection scale function fluctuation theory

Citation

Avram, Florin; Palmowski, Zbigniew; Pistorius, Martijn R. On the optimal dividend problem for a spectrally negative Lévy process. Ann. Appl. Probab. 17 (2007), no. 1, 156--180. doi:10.1214/105051606000000709. http://projecteuclid.org/euclid.aoap/1171377180.


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