New insights and augmented Lagrangian algorithm for optimal portfolio liquidation with market impact

doi:10.1111/itor.13219

	New insights and augmented Lagrangian algorithm for optimal portfolio liquidation with market impact
	Xu, Fengmin 1; Li, Xuepeng 1; Dai, Yu-Hong 2,3; Wang, Meihua 4
刊名	INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH
	2022-10-12
页码	25
关键词	augmented Lagrangian algorithm equity and liability optimal portfolio liquidation price impact
ISSN号	0969-6016
DOI	10.1111/itor.13219
英文摘要	In 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.
资助项目	National Natural Science Foundation of China[11971372] ; National Natural Science Foundation of China[11631013]
WOS研究方向	Business & Economics ; Operations Research & Management Science
语种	英语
出版者	WILEY
WOS记录号	WOS:000866135300001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60853]
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Fengmin
作者单位	1.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
推荐引用方式 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.