On the optimal dividend problem for a spectrally negative Levy process

• 成果类型: Article
• 署名作者: Avram, Florin; Palmowski, Zbigniew; Pistorius, Martijn R.
• 署名单位: Universite de Pau et des Pays de l'Adour; University of Wroclaw; University of London; King's College London
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051606000000709
• 发表日期: 2007
• 页码: 156-180
• 关键词: fluctuation theory; ergodicity; EXIT

摘要

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.