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The Geometry of Constant Function Market Makers

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arxiv 2308.08066 v1 pith:O6O75L7K submitted 2023-08-15 math.OC q-fin.MFq-fin.TR

Guillermo Angeris , Tarun Chitra , Theo Diamandis , Alex Evans , Kshitij Kulkarni This is my paper · ORCID
classification math.OCq-fin.MFq-fin.TR
keywords functiontradingcfmmsgeneralgeometricmanyresultscfmm
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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'.

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Cited by 2 Pith papers

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