L'{e}vy过程及其在金融中的应用

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

摘要翻译：
这些讲义旨在以一种非正式和直观的方式介绍L\'{e}vy过程，该领域的非专业人士可以使用。在第一部分中，我们着重讨论了L{e}vy过程的理论。我们分析了L\'{e}vy过程的一个“玩具”例子，即。一个L{e}vy跳扩散，它对L{e}vy过程的分布和路径结构提供了重要的洞察力。然后，我们给出了关于L{e}vy过程的几个重要结果，如无限整除性和L{e}vy-Khintchine公式、L{e}Vy-It{o}分解、L{e}vy过程的It{o}公式和Girsanov变换。本文提供了一些证明（草图），但仍省略了大部分证明，读者只参考课本。在第二部分，我们把注意力转向了L{e}vy过程在金融建模和期权定价中的应用。我们讨论了如何用L{e}vy过程来建模资产的价格过程，并简要说明了市场的不完全性。本文从L{e}vy过程的角度对文献中常用的模型进行了讨论，并讨论了金融衍生品定价的三种方法。最后，从应用到市场数据中给出了一些指示性证据。
---
英文标题：
《An introduction to L\'{e}vy processes with applications in finance》
---
作者：
Antonis Papapantoleon
---
最新提交年份：
2008
---
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
--
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
--

---
英文摘要：
  These lectures notes aim at introducing L\'{e}vy processes in an informal and intuitive way, accessible to non-specialists in the field. In the first part, we focus on the theory of L\'{e}vy processes. We analyze a `toy' example of a L\'{e}vy process, viz. a L\'{e}vy jump-diffusion, which yet offers significant insight into the distributional and path structure of a L\'{e}vy process. Then, we present several important results about L\'{e}vy processes, such as infinite divisibility and the L\'{e}vy-Khintchine formula, the L\'{e}vy-It\^{o} decomposition, the It\^{o} formula for L\'{e}vy processes and Girsanov's transformation. Some (sketches of) proofs are presented, still the majority of proofs is omitted and the reader is referred to textbooks instead. In the second part, we turn our attention to the applications of L\'{e}vy processes in financial modeling and option pricing. We discuss how the price process of an asset can be modeled using L\'{e}vy processes and give a brief account of market incompleteness. Popular models in the literature are presented and revisited from the point of view of L\'{e}vy processes, and we also discuss three methods for pricing financial derivatives. Finally, some indicative evidence from applications to market data is presented.
---
PDF链接：
https://arxiv.org/pdf/0804.0482

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：Applications Divisibility Quantitative introduction Differential 方式 process applications 给出 课本