A Mean Field Game of Optimal Portfolio Liquidation

Guanxing Fu (), Paulwin Graewe (), Ulrich Horst () and Alexandre Popier ()
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Guanxing Fu: Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
Paulwin Graewe: Deloitte Consulting GmbH, 10719 Berlin, Germany
Ulrich Horst: Department of Mathematics and School of Business and Economics, Humboldt-Universität zu Berlin, 10099 Berlin, Germany
Alexandre Popier: Laboratoire Manceau de Mathématiques, Le Mans Université, 72058 Le Mans Cedex 9, France

Mathematics of Operations Research, 2021, vol. 46, issue 4, 1250-1281

Abstract: 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.

Keywords: mean field game; portfolio liquidation; continuation method; singular FBSDE; 93E20; 91B70; 60H30; Primary: Games/group decisions: stochastic; secondary: finance: portfolio; dynamic programming/optimal control: applications; probability: stochastic model applications (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:46:y:2021:i:4:p:1250-1281

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