英文标题：
《Generalized Expected Discounted Penalty Function at General Drawdown for
L\\\'{e}vy Risk Processes》
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作者：
Wenyuan Wang, Ping Chen, Shuanming Li
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最新提交年份：
2019
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英文摘要：
This paper considers an insurance surplus process modeled by a spectrally negative L\\\'{e}vy process. Instead of the time of ruin in the traditional setting, we apply the time of drawdown as the risk indicator in this paper. We study the joint distribution of the time of drawdown, the running maximum at drawdown, the last minimum before drawdown, the surplus before drawdown and the surplus at drawdown (may not be deficit in this case), which generalizes the known results on the classical expected discounted penalty function in Gerber and Shiu (1998). The results have semi-explicit expressions in terms of the $q$-scale functions and the L\\\'{e}vy measure associated with the L\\\'{e}vy process. As applications, the obtained result is applied to recover results in the literature and to obtain new results for the Gerber-Shiu function at ruin for risk processes embedded with a loss-carry-forward taxation system or a barrier dividend strategy. Moreover, numerical examples are provided to illustrate the results.
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中文摘要：
本文考虑一个由谱负L{e}vy过程建模的保险盈余过程。本文采用提款时间作为风险指标，取代了传统情况下的破产时间。我们研究了水位下降时间、水位下降时的运行最大值、水位下降前的最后一个最小值、水位下降前的盈余和水位下降时的盈余（在这种情况下可能不是赤字）的联合分布，这推广了Gerber和Shiu（1998）中关于经典预期折现惩罚函数的已知结果。结果在$q$-尺度函数和与L{e}vy过程相关的L{e}vy度量方面具有半显式表达式。作为应用，将所得结果用于恢复文献中的结果，并获得嵌入亏损结转税制或障碍红利策略的风险过程的破产时Gerber-Shiu函数的新结果。此外，还提供了数值例子来说明结果。
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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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