Abstract
We 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.
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.
Original language | English |
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Pages (from-to) | 1-44 |
Number of pages | 44 |
Journal | Mathematical Finance |
DOIs | |
Publication status | Published - 21 Dec 2023 |
Keywords
- absorption
- mean-field game
- Nash equilibrium
- nonlinear integral equations
- portfolio liquidation