基于熵散度的金融模型中肥尾的引入 措施

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：
在现有的金融文献中，基于熵的思想已被提出用于投资组合优化、期权定价模型校正以及不完全市场中定价测度的确定。抽象的问题对应于寻找一个概率测度，该测度在满足对基础资产函数的某些矩约束的情况下，使相对于已知测度的相对熵（也称为$I$-散度）最小。本文证明了在$I$-散度下，当基础资产具有胖尾分布时，最优解可能不存在，而胖尾分布在金融实践中是普遍存在的。我们注意到，如果使用“多项式散度”，这个缺点可以得到纠正。这种散度可以看作是与众所周知的（相对的）Tsallis或（相对的）Renyi熵等价的。我们讨论了这一新的优化问题的存在性和唯一性问题，以及在不同目标下最优解的性质。当相关约束包括资产函数的边际分布约束时，我们还确定了在$I$-散度和多项式-散度下的最优解结构。将这些结果应用于一个简单的期权价格模型校正问题以及Markowitz框架下的投资组合模型，我们注意到一个合理的观点，即特定的资产组合具有严重的尾部损失，可能导致所有资产的尾部分布更胖和更合理。
---
英文标题：
《Incorporating fat tails in financial models using entropic divergence
  measures》
---
作者：
Santanu Dey and Sandeep Juneja
---
最新提交年份：
2012
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
--
一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
--
一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
--

---
英文摘要：
  In the existing financial literature, entropy based ideas have been proposed in portfolio optimization, in model calibration for options pricing as well as in ascertaining a pricing measure in incomplete markets. The abstracted problem corresponds to finding a probability measure that minimizes the relative entropy (also called $I$-divergence) with respect to a known measure while it satisfies certain moment constraints on functions of underlying assets. In this paper, we show that under $I$-divergence, the optimal solution may not exist when the underlying assets have fat tailed distributions, ubiquitous in financial practice. We note that this drawback may be corrected if `polynomial-divergence' is used. This divergence can be seen to be equivalent to the well known (relative) Tsallis or (relative) Renyi entropy. We discuss existence and uniqueness issues related to this new optimization problem as well as the nature of the optimal solution under different objectives. We also identify the optimal solution structure under $I$-divergence as well as polynomial-divergence when the associated constraints include those on marginal distribution of functions of underlying assets. These results are applied to a simple problem of model calibration to options prices as well as to portfolio modeling in Markowitz framework, where we note that a reasonable view that a particular portfolio of assets has heavy tailed losses may lead to fatter and more reasonable tail distributions of all assets.
---
PDF链接：
https://arxiv.org/pdf/1203.0643

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：金融模型 Quantitative distribution Optimization Applications may 校正 entropy divergence 定价