英文标题：
《Power identities for L\\\'evy risk models under taxation and capital
injections》
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作者：
Hansjoerg Albrecher and Jevgenijs Ivanovs
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最新提交年份：
2014
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英文摘要：
In this paper we study a spectrally negative L\\\'evy process which is refracted at its running maximum and at the same time reflected from below at a certain level. Such a process can for instance be used to model an insurance surplus process subject to tax payments according to a loss-carry-forward scheme together with the flow of minimal capital injections required to keep the surplus process non-negative. We characterize the first passage time over an arbitrary level and the cumulative amount of injected capital up to this time by their joint Laplace transform, and show that it satisfies a simple power relation to the case without refraction. It turns out that this identity can also be extended to a certain type of refraction from below. The net present value of tax collected before the cumulative injected capital exceeds a certain amount is determined, and a numerical illustration is provided.
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中文摘要：
在本文中，我们研究了一个光谱负的列维过程，它在其最大运行时被折射，同时在一定水平上从下方反射。例如，这种过程可用于对保险盈余过程建模，该过程根据损失结转计划纳税，以及保持盈余过程非负所需的最小资本注入流。我们通过联合拉普拉斯变换刻画了任意水平上的首次通过时间和到目前为止的累计注入资本量，并表明它满足一个简单的幂函数关系。事实证明，这个恒等式也可以从下面延伸到某种类型的折射。确定了累计注入资本超过一定数额之前征收的税款的净现值，并提供了数字说明。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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