恒定函数做市商的几何学
The Geometry of Constant Function Market Makers
AI总结：
本文为恒定函数做市商建立一般几何框架，证明其存在唯一非递减、凹且齐次的规范交易函数，并通过锥对偶等结果推广至非路径无关情形。
摘要：
恒定函数做市商（CFMM）是加密货币代币最受欢迎的一类去中心化交易场所。本文提出了一个非常一般的几何框架（或称“公理”），它涵盖并推广了文献中关于 CFMM 的许多已知结果，而不需要可微性或齐次性等强条件。该框架的一个特别推论是，每个 CFMM 都具有一个（唯一的）规范交易函数，该函数非递减、凹且齐次，这表明许多仅针对齐次交易函数已知的结果实际上具有完全的一般性。我们还证明了 CFMM 满足若干直观的几何复合规则，并通过锥对偶对投资组合价值函数与交易函数的等价性给出了新的证明。许多结果被扩展到不假设 CFMM 路径无关、而只允许一笔交易的一般情形。最后，我们证明所有“路径无关”的 CFMM 都具有一种简单的几何描述，该描述不依赖于任何“交易历史”的概念。
英文摘要：
Constant function market makers (CFMMs) are the most popular type of decentralized trading venue for cryptocurrency tokens. In this paper, we give a very general geometric framework (or 'axioms') which encompass and generalize many of the known results for CFMMs in the literature, without requiring strong conditions such as differentiability or homogeneity. One particular consequence of this framework is that every CFMM has a (unique) canonical trading function that is nondecreasing, concave, and homogeneous, showing that many results known only for homogeneous trading functions are actually fully general. We also show that CFMMs satisfy a number of intuitive and geometric composition rules, and give a new proof, via conic duality, of the equivalence of the portfolio value function and the trading function. Many results are extended to the general setting where the CFMM is not assumed to be path-independent, but only one trade is allowed. Finally, we show that all 'path-independent' CFMMs have a simple geometric description that does not depend on any notion of a 'trading history'.
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。
