发帖
雷达卡
英文标题：
《Classification of the Bounds on the Probability of Ruin for L{\\\'e}vy
Processes with Light-tailed Jumps》
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作者：
J\\\'er\\^ome Spielmann (LAREMA)
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最新提交年份：
2018
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英文摘要：
In this note, we study the ultimate ruin probabilities of a real-valued L{\\\'e}vy process X with light-tailed negative jumps. It is well-known that, for such L{\\\'e}vy processes, the probability of ruin decreases as an exponential function with a rate given by the root of the Laplace exponent, when the initial value goes to infinity. Under the additional assumption that X has integrable positive jumps, we show how a finer analysis of the Laplace exponent gives in fact a complete description of the bounds on the probability of ruin for this class of L{\\\'e}vy processes. This leads to the identification of a case that is not considered in the literature and for which we give an example. We then apply the result to various risk models and in particular the Cram{\\\'e}r-Lundberg model perturbed by Brownian motion.
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中文摘要：
在本文中，我们研究了具有轻尾负跳的实值L{e}vy过程X的最终破产概率。众所周知，对于这样的L{e}vy过程，当初始值趋于无穷大时，破产概率作为指数函数递减，其速率由拉普拉斯指数的根给出。在X具有可积正跳跃的附加假设下，我们展示了拉普拉斯指数的更精细分析如何给出这类L{e}vy过程破产概率界的完整描述。这导致了文献中未考虑的案例的识别，我们给出了一个示例。然后，我们将结果应用于各种风险模型，尤其是受布朗运动扰动的Cram{e}r-Lundberg模型。
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分类信息：
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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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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