摘要翻译：
本文研究了一个保险公司的最优股利分配问题，该保险公司的风险过程演化为一个谱负的L{e}vy过程（在没有股利支付的情况下）。本公司管理层被假定控制股息支付的时间和规模。目标是最大限度地增加直到破产时刻收到的预期累积贴现股利支付和破产时刻的罚款支付之和，这是破产时缺口大小的增函数；此外，拿出股息可能会有固定成本。给出了相应的随机控制问题的完整解。证明了该值函数是HJB方程的唯一随机解和逐点最小随机超解。此外，根据特定的Gerber-Shiu函数，给出了单个红利带策略最优性的充要条件。并对一些具体实例进行了分析。
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英文标题：
《On Gerber-Shiu functions and optimal dividend distribution for a
  L\'{e}vy risk process in the presence of a penalty function》
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作者：
F. Avram, Z. Palmowski, M. R. Pistorius
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最新提交年份：
2015
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
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英文摘要：
  This paper concerns an optimal dividend distribution problem for an insurance company whose risk process evolves as a spectrally negative L\'{e}vy 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.
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PDF链接：
https://arxiv.org/pdf/1110.4965