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Ergodic optimal liquidations in DeFi

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  • Jialun Cao
  • David v{S}iv{s}ka

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.

Suggested Citation

  • Jialun Cao & David v{S}iv{s}ka, 2024. "Ergodic optimal liquidations in DeFi," Papers 2411.19637, arXiv.org.
    • Handle: RePEc:arx:papers:2411.19637
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    References listed on IDEAS

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    1. Jialun Cao & David v{S}iv{s}ka & Lukasz Szpruch & Tanut Treetanthiploet, 2024. "Logarithmic regret in the ergodic Avellaneda-Stoikov market making model," Papers 2409.02025, arXiv.org.
    2. Weston Barger & Matthew Lorig, 2019. "Optimal Liquidation Under Stochastic Price Impact," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-28, March.
    3. Gur Huberman & Werner Stanzl, 2005. "Optimal Liquidity Trading," Review of Finance, Springer, vol. 9(2), pages 165-200, June.
    4. He, Hua & Mamaysky, Harry, 2005. "Dynamic trading policies with price impact," Journal of Economic Dynamics and Control, Elsevier, vol. 29(5), pages 891-930, May.
    5. Olivier Guéant & Iuliia Manziuk, 2020. "Optimal control on graphs: existence, uniqueness, and long-term behavior," Post-Print hal-03252606, HAL.
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