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Article Dans Une Revue Mathematics of Operations Research Année : 2021

A Mean Field Game of Optimal Portfolio Liquidation

Guanxing Fu
Paulwin Graewe
  • Fonction : Auteur
Ulrich Horst
Alexandre Popier

Résumé

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 forward-backward stochastic differential equation (FBSDE) with a possibly singular terminal condition on the backward component or, equivalently, in terms of an FBSDE with a finite terminal value yet a singular driver. Extending the method of continuation to linear-quadratic FBSDEs with a singular driver, we prove that the MFG has a unique solution. Our existence and uniqueness result allows proving that the MFG with a possibly singular terminal condition can be approximated by a sequence of MFGs with finite terminal values.

Dates et versions

hal-03663072 , version 1 (09-05-2022)

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Citer

Guanxing Fu, Paulwin Graewe, Ulrich Horst, Alexandre Popier. A Mean Field Game of Optimal Portfolio Liquidation. Mathematics of Operations Research, 2021, 46 (4), pp.1250-1281. ⟨10.1287/moor.2020.1094⟩. ⟨hal-03663072⟩
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