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

Guanxing Fu, Ulrich Horst, Xiaonyu Xia (Corresponding Author)

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

We consider a mean-field control problem with cadlag 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.
Original languageEnglish
Pages (from-to)1-29
Number of pages29
JournalMathematics of Operations Research
DOIs
Publication statusPublished - 30 Oct 2023

Keywords

  • mean-field control
  • semimartingale strategy
  • portfolio liquidation

Fingerprint

Dive into the research topics of 'A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies'. Together they form a unique fingerprint.

Cite this