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We consider a mean-field control problem with c\`adl\`ag semimartingalestrategies arising in portfolio liquidation models with transient market impactand self-exciting order flow. We show that the value function depends on thestate process only through its law, and that it is of linear-quadratic form andthat its coefficients satisfy a coupled system of non-standard Riccati-typeequations. The Riccati equations are obtained heuristically by passing to thecontinuous-time limit from a sequence of discrete-time models. A sophisticatedtransformation shows that the system can be brought into standard Riccati formfrom which we deduce the existence of a global solution. Our analysis showsthat the optimal strategy jumps only at the beginning and the end of thetrading period.

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