On the optimal dividend problem for a spectrally negative Lévy process

Florin Avram (1) , Zbigniew Palmowski (2) , Martijn Pistorius

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Mathematical Institute, University of Wroclaw

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.

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

Domaines: Probabilités [math.PR]

Florin Avram, Zbigniew Palmowski, Martijn Pistorius. On the optimal dividend problem for a spectrally negative Lévy process. 2006. ⟨hal-00220389⟩