A Mean-Field Game of Market Entry: Portfolio Liquidation with Trading Constraints
arxiv(2024)
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 initially short position of stocks are only allowed to
buy while players with an initially 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 non-linear 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.
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