Ergodic optimal liquidations in DeFi

ArXiv ID: 2411.19637 “View on arXiv”

Authors: Unknown

Abstract

We address the liquidation problem arising from the credit risk management in decentralised finance (DeFi) by formulating it as an ergodic optimal control problem. In decentralised derivatives exchanges, liquidation is triggered whenever the parties fail to maintain sufficient collateral for their open positions. Consequently, effectively managing and liquidating disposal of positions accrued through liquidations is a critical concern for decentralised derivatives exchanges. By simplifying the model (linear temporary and permanent price impacts, simplified cash balance dynamics), we derive the closed-form solutions for the optimal liquidation strategies, which balance immediate executions with the temporary and permanent price impacts, and the optimal long-term average reward. Numerical simulations further highlight the effectiveness of the proposed optimal strategy and demonstrate that the simplified model closely approximates the original market environment. Finally, we provide the method for calibrating the parameters in the model from the available data.

Keywords: Optimal Control, DeFi Liquidation, Credit Risk Management, Price Impact Modeling, Ergodic Control, DeFi (Decentralized Finance)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rads
• Why: The paper derives closed-form solutions using advanced ergodic control and stochastic calculus, indicating high mathematical complexity. While it includes numerical simulations and a calibration method, the core contribution is a theoretical model with simplifications (linear price impacts, symmetric Poisson processes) that is not backtested on real DeFi market data, placing it closer to theoretical research than empirical finance.

  flowchart TD
    A["Research Goal: Solve<br>Ergodic Optimal Liquidation<br>in DeFi Credit Risk"]
    
    B["Methodology: Ergodic Optimal Control<br>with Linear Price Impacts"]
    
    C["Inputs & Model Simplification<br>- Cash Balance Dynamics<br>- Linear Temporary/Permanent Price Impact"]
    
    D["Computational Process<br>Derive Hamilton-Jacobi-Bellman<br>& Closed-Form Optimal Strategies"]
    
    E["Key Findings & Outcomes<br>1. Closed-Form Optimal Strategy<br>2. Balances Execution vs. Impact<br>3. Numerical Validation & Calibration Method<br>4. Model Approximates Market Environment"]

    A --> B
    B --> C
    C --> D
    D --> E