A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies

• 成果类型: Article
• 署名作者: Fu, Guanxing; Horst, Ulrich; Xia, Xiaonyu
• 署名单位: Hong Kong Polytechnic University; Hong Kong Polytechnic University; Humboldt University of Berlin; Humboldt University of Berlin; Wenzhou University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0174
• 发表日期: 2024
• 页码: 2356-2384
• 关键词: optimal trade execution; singular terminal condition; stochastic-control; games; REPRESENTATION; CHOICE; IMPACT; BSDEs

摘要

We consider a mean-field control problem with ca`dla`g semimartingale strategies arising in portfolio liquidation models with transient market impact and self-exciting order flow. We show that the value function depends on the state process only through its law, and we show that it is of linear-quadratic form and that its coefficients satisfy a coupled system of nonstandard Riccati-type equations. The Riccati equations are obtained heuristically by passing to the continuous-time limit from a sequence of discrete-time models. A sophisticated transformation shows that the system can be brought into standard Riccati form, from which we deduce the existence of a global solution. Our analysis shows that the optimal strategy jumps only at the beginning and the end of the trading period.