Paper: arXiv 2405.06854
Authors: C. Escudero, F. Lara, M. Sama
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.
Complexity vs Empirical Score
- Math Complexity: 7.5/10
- Empirical Rigor: 3.0/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper provides a strong theoretical contribution by generalizing constant function market maker (CFMM) conditions to non-convex quasilinear trade functions and proving arbitrage resilience. However, it lacks extensive empirical testing on real market data, relying instead on stylized numerical simulations.
Research Flowchart
flowchart TD
A[Research Goal: Analyze Optimal Trading & Arbitrage in AMMs with Quasilinear Trade Functions] --> B[Input: Multi-Asset CFMM Models & Non-Convex Quasilinear Functions]
B --> C[Methodology: Mathematical Optimization & Generalization of Convex AMM Frameworks]
C --> D[Simulations: Test Generalized Means & Numerical Trade Scenarios]
D --> E[Outcome: Established Existence Conditions for Optimal Trades]
D --> F[Outcome: Proved Robustness Against Arbitrage Replicating Convex AMMs]