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

Author

Listed:
  • Guanxing Fu

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong; Research Centre for Quantitative Finance, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

  • Ulrich Horst

    (Department of Mathematics, Humboldt University Berlin, 10099 Berlin, Germany; School of Business and Economics, Humboldt University Berlin, 10099 Berlin, Germany)

  • Xiaonyu Xia

    (College of Mathematics and Physics, Wenzhou University, Wenzhou 325035, People’s Republic of China)

Abstract

We consider a mean-field control problem with càdlàg 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.

Suggested Citation

  • Guanxing Fu & Ulrich Horst & Xiaonyu Xia, 2024. "A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies," Mathematics of Operations Research, INFORMS, vol. 49(4), pages 2356-2384, November.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:4:p:2356-2384
    DOI: 10.1287/moor.2022.0174
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