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arXiv · 1804.04911

A Mean Field Game of Optimal Portfolio Liquidation

Guanxing Fu·Paulwin Graewe·Ulrich Horst·Alexandre Popier
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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 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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Guanxing Fu, Paulwin Graewe, Ulrich Horst, Alexandre Popier. 2018-04-13. A Mean Field Game of Optimal Portfolio Liquidation. https://arxiv.org/abs/1804.04911

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