A Multi-step Approach for Minimizing Risk in Decentralized Exchanges

ArXiv ID: 2406.07200 “View on arXiv”

Authors: Unknown

Abstract

Decentralized Exchanges are becoming even more predominant in today’s finance. Driven by the need to study this phenomenon from an academic perspective, the SIAG/FME Code Quest 2023 was announced. Specifically, participating teams were asked to implement, in Python, the basic functions of an Automated Market Maker and a liquidity provision strategy in an Automated Market Maker to minimize the Conditional Value at Risk, a critical measure of investment risk. As the competition’s winning team, we highlight our approach in this work. In particular, as the dependence of the final return on the initial wealth distribution is highly non-linear, we cannot use standard ad-hoc approaches. Additionally, classical minimization techniques would require a significant computational load due to the cost of the target function. For these reasons, we propose a three-step approach. In the first step, the target function is approximated by a Kernel Ridge Regression. Then, the approximating function is minimized. In the final step, the previously discovered minimum is utilized as the starting point for directly optimizing the desired target function. By using this procedure, we can both reduce the computational complexity and increase the accuracy of the solution. Finally, the overall computational load is further reduced thanks to an algorithmic trick concerning the returns simulation and the usage of Cython.

Keywords: Automated Market Maker (AMM), Decentralized Exchanges (DEX), Conditional Value at Risk (CVaR), Kernel Ridge Regression, Liquidity Provision, Cryptocurrencies

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper presents advanced mathematical techniques including Kernel Ridge Regression and SLSQP for a non-linear optimization problem, but the empirical component is strong with implementation details, competition results, and computational optimizations like Cython.

  flowchart TD
    A["Research Goal:<br>Minimize CVaR in AMM Liquidity Provision"] --> B["Identify Challenges:<br>Non-linear Dependencies<br>High Computational Cost"]
    
    B --> C{"Three-Step Approach"}
    
    C --> D["Step 1: Approximation<br>Kernel Ridge Regression"]
    D --> E["Step 2: Minimization<br>Optimize Approximated Function"]
    E --> F["Step 3: Refinement<br>Local Optimization from Step 2 Result"]
    
    F --> G["Key Outcomes:<br>Reduced Complexity &<br>Increased Accuracy"]
    
    G --> H["Implementation Notes:<br>Algorithmic Simulation Tricks &<br>Cython for Performance"]