A Mean Field Game of Optimal Portfolio Liquidation

Guanxing Fu (1) , Paulwin Graewe (1) , Ulrich Horst (1) , Alexandre Popier (2)

1 HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin
2 LMM - Laboratoire Manceau de Mathématiques

We consider a mean field game (MFG) of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a FBSDE with possibly singular terminal condition on the backward component or, equivalently, in terms of a FBSDE with finite terminal value, yet singular driver. Extending the method of continuation to linear-quadratic FBSDE with singular driver we prove that the MFG has a unique solution. Our existence and uniqueness result allows to prove that the MFG with possibly singular terminal condition can be approximated by a sequence of MFGs with finite terminal values.

Mots clés: mean field game; portfolio liquidation; continuation method; singular FBSDE; AMS Subject Classification: 93E20; 91B70; 60H30 mean field game; mean field game

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Guanxing Fu, Paulwin Graewe, Ulrich Horst, Alexandre Popier. A Mean Field Game of Optimal Portfolio Liquidation. 2021. ⟨hal-01764399v3⟩