CSpace
Sample average approximation of CVaR-based hedging problem with a deep-learning solution
Peng, Cheng1,2; Li, Shuang1,2; Zhao, Yanlong1,2; Bao, Ying3
2021-04-01
Source PublicationNORTH AMERICAN JOURNAL OF ECONOMICS AND FINANCE
ISSN1062-9408
Volume56Pages:14
AbstractConditional Value-at-Risk (CVaR) is an extremely popular risk measure in finance and is usually optimized to reduce the risk of large losses. This paper considers the CVaR optimization problem for hedging a portfolio of derivatives with bounded constraints. We focus on minimizing the CVaR of the loss of the hedging portfolio by a deep learning solution because of its promising application to classic portfolio optimization. As the cost objective function in the deep learning framework, the CVaR does not have a closed-form expression, but it can be estimated by using the i.i.d samples average approximation method. While many works have adopted minimizing the estimated CVaR to obtain the optimal solution, they lack theoretical performance guarantees for sample-based solutions. This paper attempts to bridge this gap. On the one hand, we introduce a typical deep neural network architecture for training the optimal hedging strategies, which helps us to analyze the properties of function set for this neural network. On the other hand, we offer a sufficient condition to guarantee that the optimal strategies obtained by using the estimated CVaR can be assured in practical applications. In particular, we prove that the uniform convergence in probability of the estimated CVaR to CVaR over a set of functions, which are generated by the proposed deep neural network. Numerical experiments verify the proposed sufficient condition and demonstrate the feasibility and superiority of this approach.
KeywordConditional Value-at-Risk Hedging strategies Deep learning Theoretical guarantee Sample average approximation Uniform convergence
DOI10.1016/j.najef.2020.101325
Indexed BySCI
Language英语
WOS Research AreaBusiness & Economics
WOS SubjectBusiness, Finance ; Economics
WOS IDWOS:000631532300003
PublisherELSEVIER SCIENCE INC
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/58285
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhao, Yanlong
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, KLSC, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Ind & Commercial Bank China, Beijing 100032, Peoples R China
Recommended Citation
GB/T 7714
Peng, Cheng,Li, Shuang,Zhao, Yanlong,et al. Sample average approximation of CVaR-based hedging problem with a deep-learning solution[J]. NORTH AMERICAN JOURNAL OF ECONOMICS AND FINANCE,2021,56:14.
APA Peng, Cheng,Li, Shuang,Zhao, Yanlong,&Bao, Ying.(2021).Sample average approximation of CVaR-based hedging problem with a deep-learning solution.NORTH AMERICAN JOURNAL OF ECONOMICS AND FINANCE,56,14.
MLA Peng, Cheng,et al."Sample average approximation of CVaR-based hedging problem with a deep-learning solution".NORTH AMERICAN JOURNAL OF ECONOMICS AND FINANCE 56(2021):14.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Peng, Cheng]'s Articles
[Li, Shuang]'s Articles
[Zhao, Yanlong]'s Articles
Baidu academic
Similar articles in Baidu academic
[Peng, Cheng]'s Articles
[Li, Shuang]'s Articles
[Zhao, Yanlong]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Peng, Cheng]'s Articles
[Li, Shuang]'s Articles
[Zhao, Yanlong]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.