标题： 常数函数做市商的几何学 显示英文标题

标题： The Geometry of Constant Function Market Makers

摘要： 常数函数市场做市商（CFMMs）是加密货币代币最流行的去中心化交易场所。 在本文中，我们提供了一个非常一般的几何框架（或“公理”），涵盖了文献中许多已知的CFMM结果，并进行了推广，而无需要求如可微性或齐次性等强条件。 这个框架的一个具体结果是，每个CFMM都有一个（唯一的）规范交易函数，该函数是非递减的、凹的和齐次的，这表明许多仅针对齐次交易函数已知的结果实际上是完全普遍的。 我们还证明了CFMMs满足许多直观且几何的组合规则，并通过锥对偶性给出了投资组合价值函数和交易函数等价性的新证明。 许多结果被扩展到一般情况下，其中CFMM不假设路径无关，但只允许一次交易。 最后，我们证明了所有“路径无关”的CFMM都有一个简单的几何描述，该描述不依赖于任何“交易历史”的概念。 显示英文摘要

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'.