Insider trading with penalties, entropy and quadratic BSDEs

Paper: arXiv 2311.12743

Authors: Umut Çetin

Abstract

Kyle model in continuous time where the insider may be subject to legal penalties is considered. In equilibrium the insider internalises this legal risk by trading less aggressively. The equilibrium is characterised via the solution of a backward stochastic differential equation (BSDE) whose terminal condition is determined as the fixed point of a non-linear operator in equilibrium. The insider’s expected penalties in equilibrium is non-monotone in the fee structure and is given by the relative entropy of the law of a particular h-transformation of Brownian motion.

Complexity vs Empirical Score

• Math Complexity: 9.2/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework extending the continuous-time Kyle model of insider trading using quadratic BSDEs and relative entropy. However, as a purely theoretical contribution, it lacks empirical backtesting, datasets, or code implementations.

Research Flowchart

  flowchart TD
    A[Research Goal: Model insider trading under legal penalties via Continuous-Time Kyle Model] --> B[Inputs: Fee structure, fundamental asset value, noisy order flow]
    B --> C[Formulate Insider Portfolio & Optimization Problem]
    C --> D[Solve Quadratic BSDE for Value Function & Price Impact]
    D --> E[Determine Fixed Point of Non-Linear Operator for Equilibrium Terminal Condition]
    E --> F[Outcomes: Insider trades less aggressively; expected penalties linked to Relative Entropy of h-transformed Brownian Motion]