Solvability of the Gaussian Kyle model with imperfect information and risk aversion

ArXiv ID: 2501.16488 “View on arXiv”

Authors: Unknown

Abstract

We investigate a Kyle model under Gaussian assumptions where a risk-averse informed trader has imperfect information on the fundamental price of an asset. We show that an equilibrium can be constructed by considering an optimal transport problem that is solved under a measure that renders the utility of the informed trader martingale and a filtering problem under the historical measure.

Keywords: Kyle model, Gaussian assumptions, Optimal transport, Filtering problem, Risk-averse informed trader

Complexity vs Empirical Score

• Math Complexity: 9.2/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats
• Why: The paper is heavily theoretical, featuring advanced mathematics such as Gaussian optimal transport, filtering problems under different measures, and explicit equilibrium computations in a continuous-time Kyle model. It lacks any empirical data, backtests, or implementation details, focusing solely on theoretical solvability and equilibrium construction.

  flowchart TD
    A["Research Goal<br/>Model an equilibrium in a Gaussian Kyle model<br/>with a risk-averse informed trader and<br/>imperfect information on the fundamental price"] --> B["Key Methodology"]
    B --> B1["Construct equilibrium via<br/>Optimal Transport (OT) problem"]
    B --> B2["Solve filtering problem<br/>under historical measure"]
    B --> B3["Derive utility martingale condition<br/>under the equilibrium measure"]
    
    B1 --> C["Data/Inputs"]
    C --> C1["Gaussian assumptions on<br/>signals, noise, and price"]
    C --> C2["Utility function of the<br/>risk-averse informed trader"]
    
    C --> D["Computational Processes"]
    D --> D1["Solve OT problem to link<br/>filtered beliefs to asset price"]
    D --> D2["Apply filtering theory to<br/>update beliefs from signals"]
    D --> D3["Verify martingale property<br/>for equilibrium measure"]
    
    D --> E["Key Findings/Outcomes"]
    E --> E1["Existence of equilibrium<br/>under Gaussian assumptions"]
    E --> E2["Explicit characterization of<br/>price dynamics and trader strategies"]
    E --> E3["Integration of optimal transport<br/>and filtering for equilibrium construction"]