Paper: arXiv 2303.05783

Authors: Guanxing Fu, Paul P. Hager, Ulrich Horst

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 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 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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly sophisticated mathematical treatment of mean-field liquidation games with market drop-out constraints, solving complex non-linear integral equations. However, it is a purely theoretical work lacking empirical validation or backtesting on real market microstructure data.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze Liquidation Games<br/>with Market Drop-out / Absorption] --> B[Model Setup: Sellers with No Round-Trips<br/>& Short Selling Constraint]
    B --> C[Derive Equilibrium Conditions via<br/>Non-linear Higher-Order Integral Equation]
    C --> D[Prove Existence & Uniqueness of Solution<br/>for Mean-Field Game MFG & N-Player Game]
    D --> E[Establish Convergence of N-Player<br/>Equilibria to Mean-Field Equilibrium]
    E --> F[Outcomes: Unique Equilibria Proved &<br/>Impact of Drop-out Constraint on Rates Illustrated]