Uniqueness and Existence of Linear Equilibrium with a Constrained Trader
Mathematical Finance
2025-08-15 v1
Abstract
We study a discrete-time financial market with a single constrained trader, competitive market makers, and noise traders. Within the class of linear equilibria, the equilibrium structure is shown to be uniquely determined by two state variables: the market maker's expectation of the trader's remaining demand and the residual demand beyond this expectation. This discrete-time uniqueness result aligns with its continuous-time analogue, indicating that the latter may emerge as the unique limit within the same class. We also prove the existence of a linear equilibrium, providing formal support to numerical and empirical findings in related work.
Cite
@article{arxiv.2508.10138,
title = {Uniqueness and Existence of Linear Equilibrium with a Constrained Trader},
author = {Heeyoung Kwon and Jin Hyuk Choi},
journal= {arXiv preprint arXiv:2508.10138},
year = {2025}
}