Paper: arXiv 2411.19637

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats

Why this score: 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.

Research Flowchart

  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

Cited References (27)

  1. Incorporating order-flow into optimal execution (2016)
  2. Algorithmic and high-frequency trading (2015)
  3. Market Impact: A systematic study of limit orders (2017)
  4. Optimal control of execution costs for portfolios (1999)
  5. Optimal execution of portfolio transactions (2001)
  6. Stochastic calculus for finance II: Continuous-time models (2004)
  7. Logarithmic regret in the ergodic A vellaneda– S toikov market making model — → 2409.02025
  8. Aave Protocol Whitepaper (2020)
and 19 more
  1. Compound: The Money Market Protocol (2019)
  2. Vega Protocol: A Decentralized Protocol for Creating and Trading Derivatives on a Fully Decentralized Network (2020)
  3. The paradox of adversarial liquidation in decentralised lending (2023)
  4. Dynamic trading policies with price impact (2005)
  5. Optimal liquidation under stochastic price impact (2019)
  6. On ergodic stochastic control (1998)
  7. dydx: A standard for decentralized margin trading and derivatives (2018)
  8. MakerDAO: The Maker Protocol Whitepaper (2021) — link
  9. Margins and Credit Risk on V ega (2019)
  10. An empirical study of defi liquidations: Incentives, risks, and instabilities (2021)
  11. Liquidations: DeFi on a Knife-edge (2021)
  12. The Financial Mathematics of Market Liquidity: From optimal execution to market making (2016)
  13. Optimal liquidity trading (2005)
  14. Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations (2001)
  15. Asymptotic solutions of H amilton– J acobi equations in E uclidean n space (2006)
  16. Large time asymptotic problems for optimal stochastic control with superlinear cost (2012)
  17. Large time behavior for some nonlinear degenerate parabolic equations (2014)
  18. Optimal control on graphs: existence, uniqueness, and long-term behavior (2020)
  19. Statistical inference (2024)

1 of 27 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.