Optimization· 2026Q1
Optimal trade characterizations in multi-asset crypto-financial markets
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- Q1SCImago
- 2026year
Short summary
This paper establishes conditions for optimal trading in automated market makers using quasilinear, non-convex trade functions, generalizing prior work and ensuring arbitrage robustness.
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Key points
- Establishes conditions for optimal trading with quasilinear, non-convex trade functions in AMMs.
- Generalizes previous AMM optimization results that assumed convexity.
- Guarantees robustness against arbitrage for AMMs designed with these functions.
- Illustrates theoretical findings with generalized means and numerical simulations.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Optimization, 2026 · DOI ↗
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Field: Information Systems
Information SystemsComputer Science