Optimal Trade Characterizations in Multi-Asset Crypto-Financial Markets

TL;DR

This paper provides a rigorous mathematical analysis of optimal trading conditions in multi-asset crypto markets using quasilinear trade functions, extending previous convexity-based models and demonstrating robustness against arbitrage.

Contribution

It generalizes the theory of constant function market makers to non-convex trade functions, enhancing robustness and applicability in crypto-financial markets.

Findings

Generalizes optimal trade conditions to non-convex functions

Shows robustness of market makers against arbitrage

Provides numerical simulations supporting theoretical results

Abstract

This work focuses on the mathematical study of constant function market makers. We rigorously establish the conditions for optimal trading under the assumption of a quasilinear, but not necessarily convex (or concave), trade function. This generalizes previous results that used convexity, and also guarantees the robustness against arbitrage of so-designed automatic market makers. The theoretical results are illustrated by families of examples given by generalized means, and also by numerical simulations in certain concrete cases. These simulations along with the mathematical analysis suggest that the quasilinear-trade-function based automatic market makers might replicate the functioning of those based on convex functions, in particular regarding their resilience to arbitrage.