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Zbl 1136.60032
Avram, Florin; Palmowski, Zbigniew; Pistorius, Martijn R.
On the optimal dividend problem for a spectrally negative Lévy process. (English)
[J] Ann. Appl. Probab. 17, No. 1, 156-180 (2007). ISSN 1050-5164

In classical collective risk theory the surplus process of an insurance company is described by the Cramer-Lundberg model, has positive first moment and has therefore the unrealistic property that it converges to infinity with probability 1. In answer to this objection, De Finetti (1957) introduced the divident barrier model, in which all surpluses a given level are transferred to a beneficiary. In mathematical finance and actuarial literature there is a good deal of work on divident barrier models. A drawback of the divident barrier model is that under this model the risk process will down-cross the level zero with probability 1. \par In this paper, the authors approach the divident problem from the point of view of a general spectrally negative Levy process. Drawing on the fluctuation theory of spectrally negative Levy processes they give an explicit analytical description of the optimal strategy in the set of barrier strategies and the corresponding value function. They conclude the paper with some explicit examples in the classical and `bail-out' setting.
[Anatoliy Swishchuk (Calgary)]

MSC 2000:: *60G51 Processes with independent increments
60J99 Markov processes
93E20 Optimal stochastic control (systems)
91B28 Finance etc.

Keywords: Levy process; divident problem; local time; reflection; scale function; fluctuation theory

Cited in: Zbl 1219.91076 Zbl 1176.60034 Zbl 1152.60344

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