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摘要翻译：
考虑两家保险公司（或同一家公司的两个分支机构）以不同的费率收取保费，然后按固定比例对每一项索赔进行分摊（为了简单起见，我们假定它们相等）。我们根据泊松过程对索赔的发生进行建模。当相应的二维风险过程首先离开正象限时达到破产。我们将考虑受控过程的两种情况：折射和脉冲控制。在第一种情况下，当二维风险过程离开固定区域时，派发红利。在第二种情况下，每当过程碰到水平线时，它就通过支付红利到正象限的某个固定点来减少，在那里它等待下一个索赔到达。在这两个模型中，我们都计算到破产前的贴现累计股利支付。本文首次试图了解两个投资组合的相关性对联合最优股利支付策略的影响。例如，在比例再保险中，可以观察到一个有趣的现象，即最优障碍的选择取决于初始准备金。这与一维Cram\'{e}r-Lundberg模型形成鲜明对比，在该模型中，对于所有初始储量，屏障的最优选择是一致的。
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英文标题：
《De Finetti's dividend problem and impulse control for a two-dimensional
insurance risk process》
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作者：
Irmina Czarna and Zbigniew Palmowski
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最新提交年份：
2011
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分类信息：
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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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：
Consider two insurance companies (or two branches of the same company) that receive premiums at different rates and then split the amount they pay in fixed proportions for each claim (for simplicity we assume that they are equal). We model the occurrence of claims according to a Poisson process. The ruin is achieved when the corresponding two-dimensional risk process first leaves the positive quadrant. We will consider two scenarios of the controlled process: refraction and impulse control. In the first case the dividends are payed out when the two-dimensional risk process exits the fixed region. In the second scenario, whenever the process hits the horizontal line, it is reduced by paying dividends to some fixed point in the positive quadrant where it waits for the next claim to arrive. In both models we calculate the discounted cumulative dividend payments until the ruin. This paper is the first attempt to understand the effect of dependencies of two portfolios on the joint optimal strategy of paying dividends. For example in case of proportional reinsurance one can observe the interesting phenomenon that choice of the optimal barrier depends on the initial reserves. This is in contrast with the one-dimensional Cram\'{e}r-Lundberg model where the optimal choice of the barrier is uniform for all initial reserves.
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PDF链接：
https://arxiv.org/pdf/0906.2100
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