A state-constrained differential game arising in optimal portfolio liquidation
Optimization and Control
2015-07-08 v5 Trading and Market Microstructure
Abstract
We consider risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions for finite and infinite time horizons. We prove existence and uniqueness of Nash equilibria and give closed-form solutions in some special cases. We also analyze qualitative properties of the equilibrium strategies and provide corresponding financial interpretations.
Keywords
Cite
@article{arxiv.1312.7360,
title = {A state-constrained differential game arising in optimal portfolio liquidation},
author = {Alexander Schied and Tao Zhang},
journal= {arXiv preprint arXiv:1312.7360},
year = {2015}
}