Paper: arXiv 2307.09392

Abstract

In the dynamic discrete-time trading setting of Kyle (1985), we prove that Kyle’s equilibrium model is stable when there are one or two trading times. For three or more trading times, we prove that Kyle’s equilibrium is not stable. These theoretical results are proven to hold irrespectively of all Kyle’s input parameters.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is heavily theoretical, proving stability properties of a canonical microstructure model using advanced functional analysis and fixed-point theory, with no empirical data or backtesting involved. Its results are purely analytical and abstract, making it typical of theoretical finance research.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Is Kyle's equilibrium stable?"] --> B["Methodology:<br>Mathematical Proofs"]
  B --> C["Input Parameters:<br>Kyle's model assumptions"]
  C --> D["Analysis of Trading Times:<br>N = 1, 2, 3, ..."]
  D --> E{"Stable?"}
  E -- N = 1, 2 --> F["Outcome: STABLE"]
  E -- N >= 3 --> G["Outcome: NOT STABLE"]
  F --> H["Conclusion:<br>Stability depends on trading periods"]
  G --> H