英文标题：
《On occupation times in the red of L\\\'evy risk models》
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作者：
David Landriault, Bin Li and Mohamed Amine Lkabous
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最新提交年份：
2019
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英文摘要：
In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level $0$) up to an (independent) exponential horizon for spectrally negative L\\\'{e}vy risk processes and refracted spectrally negative L\\\'{e}vy risk processes. This result improves the existing literature in which only the Laplace transforms are known. Due to the close connection between occupation time and many other quantities, we provide a few applications of our results including future drawdown, inverse occupation time, Parisian ruin with exponential delay, and the last time at running maximum. By a further Laplace inversion to our results, we obtain the distribution of the occupation time up to a finite time horizon for refracted Brownian motion risk process and refracted Cram\\\'{e}r-Lundberg risk model with exponential claims.
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中文摘要：
本文得到了光谱负L{e}vy风险过程和折射光谱负L{e}vy风险过程在（独立）指数范围内的红色（低于0美元）占用时间分布的解析表达式。这一结果改进了现有文献中只知道拉普拉斯变换的情况。由于占用时间与许多其他量之间的密切联系，我们提供了我们的结果的一些应用，包括未来水位下降、反向占用时间、指数延迟的巴黎破产和最后一次运行最大时间。通过对我们的结果进一步的拉普拉斯反演，我们得到了折射布朗运动风险过程和折射Cram{e}r-Lundberg指数索赔风险模型在有限时间范围内的占用时间分布。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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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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