Mean‐field liquidation games with market drop‐out

Abstract

AbstractWe consider a novel class of portfolio liquidation games with market drop‐out (“absorption”). More precisely, we consider mean‐field and finite player liquidation games where a player drops out of the market when her position hits zero. In particular, round‐trips are not admissible. This can be viewed as a no statistical arbitrage condition. In a model with only sellers, we prove that the absorption condition is equivalent to a short selling constraint. We prove that equilibria (both in the mean‐field and the finite player game) are given as solutions to a 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 in the MFG and the existence of a unique equilibrium in the N‐player game. We establish the convergence of the equilibria in the finite player games to the obtained mean‐field equilibrium and illustrate the impact of the drop‐out constraint on equilibrium trading rates.