# A state-constrained differential game arising in optimal portfolio liquidation

arXiv: https://arxiv.org/abs/1312.7360 · HTML: https://mlsanity.com/paper/1312.7360/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2013.

## Built on by (most cited first, 3 of 3)

- [Memory-Induced Supra-Competitive Outcomes Between Deep Reinforcement Learning Agents in Optimal Trade Execution](https://mlsanity.com/paper/2605.20348/) (2026)
- [Deviations from the Nash equilibrium in a two-player optimal execution game with reinforcement learning](https://mlsanity.com/paper/2408.11773/) (2024)
- [Beyond Supra-Competitive Outcomes: Collusive Behaviour in Deep Reinforcement Learning for Optimal Execution Games](https://mlsanity.com/paper/2610.00619/) (2026)

## Abstract (arXiv)

We consider n 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.