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Concave Continuation: Linking Routing to Arbitrage

Ruichao Jiang, Long Wen

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.

Concave Continuation: Linking Routing to Arbitrage

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.

Paper Structure

This paper contains 5 sections, 1 theorem, 16 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Local Conservation Law
  5. Concave Continuation

Key Result

Proposition 5

Under the assumptions in §sec:background, the concave continuation satisfies:

Figures (1)

  • Figure 1: AMM $i$ flips direction

Theorems & Definitions (6)

  • Definition 1: Trade function
  • Remark
  • Example 2: Trade functions in Uniswap V2
  • Definition 3: Local conservation law
  • Definition 4: Concave continuation
  • Proposition 5: Properties of the concave continuation