Ergodic optimal liquidations in DeFi

TL;DR

This paper formulates the liquidation problem in DeFi as an ergodic optimal control problem, deriving closed-form solutions for optimal strategies that balance immediate liquidation costs with long-term rewards.

Contribution

It introduces a simplified model for DeFi liquidations, providing closed-form solutions and a calibration method, advancing the understanding of optimal liquidation strategies in decentralized finance.

Findings

Optimal strategies effectively balance immediate and long-term costs.

Simplified model closely approximates real market conditions.

Numerical simulations validate the strategy's effectiveness.

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.