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摘要翻译：
本文研究了一个保险公司的最优股利问题，该保险公司的无控制准备金过程演化为一个经典的Crm{e}r-Lundberg过程。公司可以选择将部分盈余投资于布莱克-斯科尔斯金融市场。目标是找到一个由投资和股利支付政策组成的策略，该策略使截至破产时的累积预期贴现股利支付最大化。我们证明了最优值函数是关联的二阶积分微分Hamilton-Jacobi-Bellman方程的最小粘性解。我们研究了最优值函数的正则性。我们证明了最优股利支付策略具有带结构。我们找到了一种构造候选解的方法，并得到了一个验证结果来检查最优性。最后，我们给出了一个最优股利策略不是障碍且最优值函数不是两次连续可微的例子。
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英文标题：
《Optimal investment policy and dividend payment strategy in an insurance
company》
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作者：
Pablo Azcue, Nora Muler
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最新提交年份：
2010
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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：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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英文摘要：
We consider in this paper the optimal dividend problem for an insurance company whose uncontrolled reserve process evolves as a classical Cram\'{e}r--Lundberg process. The firm has the option of investing part of the surplus in a Black--Scholes financial market. The objective is to find a strategy consisting of both investment and dividend payment policies which maximizes the cumulative expected discounted dividend pay-outs until the time of bankruptcy. We show that the optimal value function is the smallest viscosity solution of the associated second-order integro-differential Hamilton--Jacobi--Bellman equation. We study the regularity of the optimal value function. We show that the optimal dividend payment strategy has a band structure. We find a method to construct a candidate solution and obtain a verification result to check optimality. Finally, we give an example where the optimal dividend strategy is not barrier and the optimal value function is not twice continuously differentiable.
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PDF链接：
https://arxiv.org/pdf/1010.4988
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