论文标题
查找正确的曲线：恒定功能做市商的最佳设计
Finding the Right Curve: Optimal Design of Constant Function Market Makers
论文作者
论文摘要
恒定功能做市商（CFMM）是创建交易市场，已在预测市场中有效部署的工具，现在在分散的金融生态系统中特别突出。我们表明，对于任何关于未来资产价格的信念，都存在最佳的CFMM交易功能，可最大程度地提高CFMM可以解决的交易部分。我们制定一个凸面程序来计算此最佳交易功能。因此，该计划为营销商提供了一个可访问的框架，可以将基础资产的未来价格汇总到最大资本效率CFMM的交易功能中。 我们的凸优化框架进一步扩展，以捕获费用收入，套利损失和流动性提供者的机会成本之间的权衡。分析该计划表明，对利润和损失的考虑如何导致定性不同的最佳交易功能。我们的模型还解释了在实践中出现的CFMM设计的多样性。我们表明，对我们的凸面计划的仔细分析可以推断出市政机构对未来资产价格的信念，并表明这些信念反映了几种广泛使用的CFMM的民间传说直觉。制定该计划需要关于CFMM流动性的新概念，而核心技术挑战在于分析对无限二维Banach空间优化的KKT条件。
Constant Function Market Makers (CFMMs) are a tool for creating exchange markets, have been deployed effectively in prediction markets, and are now especially prominent in the Decentralized Finance ecosystem. We show that for any set of beliefs about future asset prices, an optimal CFMM trading function exists that maximizes the fraction of trades that a CFMM can settle. We formulate a convex program to compute this optimal trading function. This program, therefore, gives a tractable framework for market-makers to compile their belief function on the future prices of the underlying assets into the trading function of a maximally capital-efficient CFMM. Our convex optimization framework further extends to capture the tradeoffs between fee revenue, arbitrage loss, and opportunity costs of liquidity providers. Analyzing the program shows how the consideration of profit and loss leads to a qualitatively different optimal trading function. Our model additionally explains the diversity of CFMM designs that appear in practice. We show that careful analysis of our convex program enables inference of a market-maker's beliefs about future asset prices, and show that these beliefs mirror the folklore intuition for several widely used CFMMs. Developing the program requires a new notion of the liquidity of a CFMM, and the core technical challenge is in the analysis of the KKT conditions of an optimization over an infinite-dimensional Banach space.
