A Mean Field Game of Optimal Portfolio Liquidation
Optimization and Control
2021-01-26 v3 Probability
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.
Keywords
Cite
@article{arxiv.1804.04911,
title = {A Mean Field Game of Optimal Portfolio Liquidation},
author = {Guanxing Fu and Paulwin Graewe and Ulrich Horst and Alexandre Popier},
journal= {arXiv preprint arXiv:1804.04911},
year = {2021}
}