Key Takeaways
This paper gives 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.
Finally, the paper shows 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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