英文标题：
《On the Optimal Dividend Problem for Insurance Risk Models with
Surplus-Dependent Premiums》
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作者：
Ewa Marciniak and Zbigniew Palmowski
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最新提交年份：
2016
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英文摘要：
This paper concerns an optimal dividend distribution problem for an insurance company with surplus-dependent premium. In the absence of dividend payments, such a risk process is a particular case of so-called piecewise deterministic Markov processes. The control mechanism chooses the size of dividend payments. The objective consists in maximazing the sum of the expected cumulative discounted dividend payments received until the time of ruin and a penalty payment at the time of ruin, which is an increasing function of the size of the shortfall at ruin. A complete solution is presented to the corresponding stochastic control problem. We identify the associated Hamilton-Jacobi-Bellman equation and find necessary and sufficient conditions for optimality of a single dividend-band strategy, in terms of particular Gerber-Shiu functions. A number of concrete examples are analyzed.
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中文摘要：
本文研究了一类保险公司的最优股利分配问题。在没有股息支付的情况下，这种风险过程是所谓的分段确定性马尔可夫过程的特例。控制机制选择股息支付的规模。目标在于使破产前收到的预期累计贴现股息支付和破产时的罚金支付之和最大化，这是破产时短缺规模的递增函数。给出了相应的随机控制问题的完整解。我们确定了相关的Hamilton-Jacobi-Bellman方程，并根据特定的Gerber-Shiu函数，找到了单红利带策略最优性的充分必要条件。分析了若干具体实例。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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