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On the optimal dividend problem for a spectrally negative Lévy process

Florin Avram 1, Zbigniew Palmowski 2, Martijn Pistorius 3

(2006)

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 amongst all admissible ones takes the form of a barrier strategy.

1 :	Laboratoire de Mathématiques et de leurs Applications de Pau (LMA-PAU)
	CNRS : UMR5142 – Université de Pau et des Pays de l'Adour [UPPA]
2 :	Mathematical Institute, University of Wroclaw
	University of Wroclaw
3 :	Department of Mathematics, King's College London
	University of London

Domaine

:

Mathématiques/Probabilités

Mots Clés : (Doubly) reflected Lévy processes – dividend problem – local time – scale functions – optimal control

hal-00220389, version 1

http://hal.archives-ouvertes.fr/hal-00220389

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Contributeur : Responsable Hal Lma-Pau <>

Soumis le : Lundi 28 Janvier 2008, 10:00:06

Dernière modification le : Lundi 28 Janvier 2008, 15:59:41