Uniqueness and Existence of Linear Equilibrium with a Constrained Trader

Paper: arXiv 2508.10138

Authors: Heeyoung Kwon, Jin Hyuk Choi

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents rigorous mathematical proofs for the structural uniqueness and existence of a linear equilibrium in a discrete-time Kyle-type model with a constrained trader. It provides valuable theoretical foundations for prior continuous-time and empirical findings, though it contains no real-world empirical data analysis or backtesting.

Research Flowchart

  flowchart TD
    A["Research Goal: Prove existence & uniqueness of linear equilibrium with a constrained trader in discrete time"] --> B["Model Inputs: Single constrained trader, competitive market makers, noise traders"]
    B --> C["Methodology: Discrete-time market microstructure modeling"]
    C --> D["State Space Reduction: Define state variables (expected remaining demand & residual demand)"]
    D --> E["Equilibrium Analysis: Prove uniqueness and existence within linear strategy class"]
    E --> F["Key Outcome: Uniqueness determined by two state variables, aligning with continuous-time limit"]
    E --> G["Key Outcome: Formal proof of existence supporting prior numerical/empirical work"]