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New insights and augmented Lagrangian algorithm for optimal portfolio liquidation with market impact
Xu, Fengmin1; Li, Xuepeng1; Dai, Yu-Hong2,3; Wang, Meihua4
2022-10-12
Source PublicationINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH
ISSN0969-6016
Pages25
AbstractIn financial markets, investors may be forced to unwind their portfolios to meet a determined leverage ratio within regulatory policy or risk management requirements. This paper studies the optimal portfolio liquidation problem with market impact. Some new insights are given into this problem, and trading orders are discussed for various financial parameters. Specifically, we establish the equivalence between equity and liability maximization. This means if one wants to maximize the equity, it is to maximize the liability and vice versa. The computational complexity of the problem is examined to be NP-hard. We expose the hidden convexity through monotonicity analysis and linearization techniques. Although good properties are established for the Lagrangian algorithm, a counter-example is constructed to show one deficiency of this algorithm. Therefore, we propose an augmented Lagrangian algorithm for solving the problem. The inverse Hessian of the augmented Lagrangian function is explicitly calculated for the subproblem solved by the projected Newton method. Meanwhile, we consider how to choose a good initial point, which is essential for seeking a high-quality solution. Some numerical results are presented, which validate the usefulness of the augmented Lagrangian algorithm.
Keywordaugmented Lagrangian algorithm equity and liability optimal portfolio liquidation price impact
DOI10.1111/itor.13219
Indexed BySCI
Language英语
Funding ProjectNational Natural Science Foundation of China[11971372] ; National Natural Science Foundation of China[11631013]
WOS Research AreaBusiness & Economics ; Operations Research & Management Science
WOS SubjectManagement ; Operations Research & Management Science
WOS IDWOS:000866135300001
PublisherWILEY
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/60854
Collection中国科学院数学与系统科学研究院
Corresponding AuthorXu, Fengmin
Affiliation1.Xi An Jiao Tong Univ, Sch Econ & Finance, Xian 710061, Peoples R China
2.Chinese Acad Sci, LSEC, Acad Math Syst Sci, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Xidian Univ, Sch Econ & Management, Xian 710126, Peoples R China
Recommended Citation
GB/T 7714
Xu, Fengmin,Li, Xuepeng,Dai, Yu-Hong,et al. New insights and augmented Lagrangian algorithm for optimal portfolio liquidation with market impact[J]. INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH,2022:25.
APA Xu, Fengmin,Li, Xuepeng,Dai, Yu-Hong,&Wang, Meihua.(2022).New insights and augmented Lagrangian algorithm for optimal portfolio liquidation with market impact.INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH,25.
MLA Xu, Fengmin,et al."New insights and augmented Lagrangian algorithm for optimal portfolio liquidation with market impact".INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH (2022):25.
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