arXiv 2212.033402022-12cs.GT

寻找正确的曲线：常函数做市商的最优设计

Finding the Right Curve: Optimal Design of Constant Function Market Makers

Mohak Goyal, Geoffrey Ramseyer, Ashish Goel, David Mazières

备注：: 31 pages

摘要：

恒定功能做市商（CFIREX）是一种创建交易所市场的工具，已在预测市场中有效部署，现在在去中心化金融生态系统中尤为突出。我们表明，对于任何一组信念的未来资产价格，最佳CFMM交易功能存在，最大限度地提高交易的CFMM可以解决的部分。我们制定了一个凸规划来计算这个最优交易函数。因此，该方案为做市商提供了一个易于处理的框架，可以将其对标的资产未来价格的信念函数编译为最大资本效率CFMM的交易函数。我们的凸优化框架进一步扩展到捕获手续费收入，套利损失和流动性提供商的机会成本之间的权衡。分析该程序显示，考虑利润和损失如何导致一个质的不同的最佳交易函数。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，仔细分析我们的凸计划，使推理的做市商的信念对未来的资产价格，并表明这些信念反映了民俗的直觉，几个广泛使用的CFcirrhosis。开发程序需要一个新的概念的CFMM的流动性，和核心的技术挑战是在无限维Banach空间的优化的KKT条件的分析。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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