Key Takeaways
This paper presents a method for constructing Constant Function Market Makers (CFMMs) whose portfolio value functions match a desired payoff.
More specifically it shows that the space of concave, nonnegative, nondecreasing, 1-homogeneous payoff functions and the space of convex CFMMs are equivalent.
This method uses only basic tools from convex analysis and is intimately related to Fenchel conjugacy, and the paper demonstrates the result by constructing trading functions corresponding to basic payoffs, as well as standard financial derivatives such as options and swaps.
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