Sample average approximation of CVaR-based hedging problem with a deep-learning solution

doi:10.1016/j.najef.2020.101325

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	Sample average approximation of CVaR-based hedging problem with a deep-learning solution
	Peng, Cheng 1,2; Li, Shuang 1,2; Zhao, Yanlong 1,2; Bao, Ying 3
	2021-04-01
发表期刊	NORTH AMERICAN JOURNAL OF ECONOMICS AND FINANCE
ISSN	1062-9408
卷号	56 页码:14
摘要	Conditional 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.
关键词	Conditional Value-at-Risk Hedging strategies Deep learning Theoretical guarantee Sample average approximation Uniform convergence
DOI	10.1016/j.najef.2020.101325
收录类别	SCI
语种	英语
WOS研究方向	Business & Economics
WOS类目	Business, Finance ; Economics
WOS记录号	WOS:000631532300003
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58285
专题	中国科学院数学与系统科学研究院
通讯作者	Zhao, Yanlong
作者单位	1.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
推荐引用方式 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.