ON GERBER-SHIU FUNCTIONS AND OPTIMAL DIVIDEND DISTRIBUTION FOR A LEVY RISK PROCESS IN THE PRESENCE OF A PENALTY FUNCTION

• 成果类型: Article
• 署名作者: Avram, F.; Palmowski, Z.; Pistorius, M. R.
• 署名单位: Universite de Pau et des Pays de l'Adour; University of Wroclaw; Imperial College London
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1038
• 发表日期: 2015
• 页码: 1868-1935
• 关键词: transaction costs; scale functions; strategies; smoothness; policies; EXIT

摘要

This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative Levy process (in the absence of dividend payments). The management of the company is assumed to control timing and size of dividend payments. The objective is to maximize the sum of the expected cumulative discounted dividend payments received until the moment of ruin and a penalty payment at the moment of ruin, which is an increasing function of the size of the shortfall at ruin; in addition, there may be a fixed cost for taking out dividends. A complete solution is presented to the corresponding stochastic control problem. It is established that the value-function is the unique stochastic solution and the pointwise smallest stochastic supersolution of the associated HJB equation. Furthermore, a necessary and sufficient condition is identified for optimality of a single dividend-band strategy, in terms of a particular Gerber-Shiu function. A number of concrete examples are analyzed.