Open AccessA Mean Field Game of Optimal Portfolio Liquidation
Author(s) -
Guanxing Fu,
Paulwin Graewe,
Ulrich Horst,
Alexandre Popier
Publication year - 2021
Publication title -
mathematics of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.619
H-Index - 83
eISSN - 1526-5471
pISSN - 0364-765X
DOI - 10.1287/moor.2020.1094
Subject(s) - mathematics , uniqueness , stochastic differential equation , terminal (telecommunication) , portfolio , sequence (biology) , differential game , continuation , singular control , mathematical optimization , mathematical analysis , optimal control , computer science , telecommunications , biology , financial economics , economics , genetics , programming language
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.
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