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

Guanxing Fu, Ulrich Horst and Xiaonyu Xia

Papers from arXiv.org

Abstract: We consider a mean-field control problem with c\`adl\`ag 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 that it is of linear-quadratic form and that its coefficients satisfy a coupled system of non-standard 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.

Date: 2022-07, Revised 2023-09
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Citations: View citations in EconPapers (2)

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