英文标题：
《Stochastic areas of diffusions and applications in risk theory》
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作者：
Zhenyu Cui
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最新提交年份：
2013
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英文摘要：
In this paper we study the stochastic area swept by a regular time-homogeneous diffusion till a stopping time. This unifies some recent literature in this area. Through stochastic time change we establish a link between the stochastic area and the stopping time of another associated time-homogeneous diffusion. Then we characterize the Laplace transform of the stochastic area in terms of the eigenfunctions of the associated diffusion. We also explicitly obtain the integer moments of the stochastic area in terms of scale and speed densities of the associated diffusion. Specifically we study in detail three stopping times: the first passage time to a constant level, the first drawdown time and the Azema-Yor stopping time. We also study the total occupation area of the diffusion below a constant level. We show applications of the results to a new structural model of default (Yildirim 2006), the Omega risk model of bankruptcy in risk analysis (Gerber, Shiu and Yang 2012), and a diffusion risk model with surplus-dependent tax (Albrecher and Hipp 2007, Li, Tang and Zhou 2013).
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中文摘要：
本文研究了正则时间齐次扩散到停止时间的随机区域。这结合了该领域的一些最新文献。通过随机时间变化，我们在随机区域和另一个相关时间齐次扩散的停止时间之间建立了联系。然后，我们用关联扩散的特征函数来描述随机区域的拉普拉斯变换。我们还明确地获得了随机区域的整数矩，即关联扩散的规模和速度密度。具体来说，我们详细研究了三种停止时间：第一次通过时间到恒定水平、第一次下降时间和Azema Yor停止时间。我们还研究了恒定水平下扩散的总占地面积。我们展示了这些结果在一个新的违约结构模型（Yildirim 2006）、风险分析中的Omega破产风险模型（Gerber、Shiu和Yang 2012）和一个具有盈余依赖税的扩散风险模型（Albrecher和Hipp 2007、Li、Tang和Zhou 2013）中的应用。
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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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