A Mean-Field Game of Market Entry: Portfolio Liquidation with Trading Constraints

• 成果类型: Article; Early Access
• 署名作者: Fu, Guanxing; Hager, Paul P.; Horst, Ulrich
• 署名单位: Hong Kong Polytechnic University; Hong Kong Polytechnic University; University of Vienna; Humboldt University of Berlin; Humboldt University of Berlin
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0820
• 发表日期: 2026-04-30
• 关键词: portfolio liquidation; mean-field game; Nash equilibrium; trading constraint; non-linear integral equations; singular terminal condition; equilibria; execution; IMPACT; BSDEs

摘要

We consider both N-player and mean-field games of optimal portfolio liquidation in which the players are not allowed to change the direction of trading. Players with an initial short position of stocks are only allowed to buy, while players with an initial long position are only allowed to sell the stock. Under suitable conditions on the model parameters, we show that the games are equivalent to games of timing where the players need to determine the optimal times of market entry and exit. We identify the equilibrium entry and exit times and prove that equilibrium mean-trading rates can be characterized in terms of the solutions to a highly nonlinear higher-order integral equation with endogenous terminal condition. We prove the existence of a unique solution to the integral equation from which we obtain the existence of a unique equilibrium both in the mean-field and the N-player game.