A Mean Field Game of Optimal Portfolio Liquidation

• 成果类型: Article
• 署名作者: Fu, Guanxing; Graewe, Paulwin; Horst, Ulrich; Popier, Alexandre
• 署名单位: Hong Kong Polytechnic University; Deloitte Touche Tohmatsu Limited; Humboldt University of Berlin; Humboldt University of Berlin; Le Mans Universite
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1094
• 发表日期: 2021
• 页码: 1250-1281
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; singular terminal condition; BSDEs; equilibria

摘要

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.