On the optimal dividend problem for a spectrally negative Lévy process

Citation
Avram, Florin et al., On the optimal dividend problem for a spectrally negative Lévy process, Annals of applied probability , 17(1), 2007, pp. 156-180
ISSN journal
10505164
Volume
17
Issue
1
Year of publication
2007
Pages
156 - 180
Database
ACNP
SICI code
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.