Concave Continuation: Linking Routing to Arbitrage

TL;DR

This paper introduces the concave continuation method to unify routing and arbitrage in automated market makers, extending trade functions to negative inputs and adapting algorithms accordingly.

Contribution

It presents a novel mathematical extension that links routing and arbitrage, enabling more comprehensive AMM trade function analysis.

Findings

Unified routing and arbitrage into a single framework

Extended one-hop transfer algorithm to the new setting

Derived from invariance of local conservation law

Abstract

We extend AMM trade functions to negative inputs via the \textit{concave continuation}, derived from the invariance of the local conservation law under allocation direction flips. This unifies routing and arbitrage into a single problem. We extend the one-hop transfer algorithm proposed in \cite{jiang} to this setting.