Concave Continuation: Linking Routing to Arbitrage

Ruichao Jiang and Long Wen

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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.

Date: 2026-04
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