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On the optimal dividend problem for a spectrally negative Levy process

Research output: Contribution to journalArticle

F Avram, Z Palmowski, M R Pistorius

Original languageEnglish
Pages (from-to)156 - 180
Number of pages25
JournalThe Annals of Applied Probability
Volume17
Issue number1
DOIs
PublishedFeb 2007

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  • King's College London

Abstract

In this paper we consider the optimal dividend problem for an insurance company whose risk process evolves as a spectrally negative Levy 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 Levy 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

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