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

Guanxing Fu (), Ulrich Horst () and Xiaonyu Xia ()
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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

Mathematics of Operations Research, 2024, vol. 49, issue 4, 2356-2384

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.

Keywords: Primary: 93E20; 91B70; 60H30; mean-field control; semimartingale strategy; portfolio liquidation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:4:p:2356-2384

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