Paper: arXiv 2512.05011

Authors: Albina Danilova, Valentin Lizhdvoy

Abstract

This paper studies a Kyle-Back model with a risk-averse insider possessing exponential utility and a dynamic stochastic signal about the asset’s terminal fundamental value. While the existing literature considers either risk-neutral insiders with dynamic signals or risk-averse insiders with static signals, we establish equilibrium when both features are present. Our approach imposes no restrictions on the magnitude of the risk aversion parameter, extending beyond previous work that requires sufficiently small risk aversion. We employ a weak conditioning methodology to construct a Schrödinger bridge between the insider’s signal and the asset price process, an approach that naturally accommodates stochastic signal evolution and removes risk aversion constraints. We derive necessary conditions for equilibrium, showing that the optimal insider strategy must be continuous with bounded variation. Under these conditions, we characterize the market-maker pricing rule and insider strategy that achieve equilibrium. We obtain explicit closed-form solutions for important cases including deterministic and quadratic signal volatilities, demonstrating the tractability of our framework.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is highly theoretical, featuring advanced mathematics like Schrödinger bridges, optimal transport, and PDEs without empirical backtesting or implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal: Find market equilibrium when\ninsider is risk-averse with dynamic signals"]

  B["Key Methodology:\n1. Kyle-Back Model Framework\n2. Weak Conditioning & Schrödinger Bridge\n3. HJB Equations"]
  
  C["Data/Inputs:\n• Exponential Utility\n• Dynamic Stochastic Signal\n• Asset Terminal Value Process"]
  
  D["Computational Process:\n• Derive necessary conditions\n• Establish continuity & bounded variation\n• Solve PDEs for pricing rule & strategy"]
  
  E["Key Findings:\n• Equilibrium characterized without\n  small risk aversion restrictions\n• Closed-form solutions for\ndeterministic & quadratic volatility cases"]
  
  A --> B
  B --> C
  C --> D
  D --> E

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