Paper: arXiv 2610.23517

Authors: Hongjian Shi, Daojing Zhai

Abstract

We develop a framework to identify and quantify arbitrage across logically related prediction-market contracts. We prove that prices outside the convex hull of admissible payoff vectors admit arbitrage and identify optimal arbitrage portfolios through integer programming. Using venue metadata and semantic analysis of resolution criteria, we recover 1.9 million logical relations and compile them into constraint systems covering more than 255,000 contracts. We replay full-depth Polymarket order books to simulate an arbitrageur executing these portfolios against resting orders. Among settled portfolios, guaranteed profit after spreads and fees equals 2.2% of committed capital, while profit at resolution reaches 3.2%. We find that arbitrage opportunities persist longer and attract less observed participation where relation discovery and execution are more costly.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 6.0/10 (capped from 9.0: no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a sophisticated mathematical framework for identifying combinatorial arbitrage, backed by extensive empirical analysis using real-world order book data. The novel approach of combining semantic analysis with integer programming to uncover and exploit arbitrage opportunities is a significant contribution. The findings are robust and clearly presented.

Research Flowchart

  flowchart TD
    A[Research Goal: Identify & Quantify Arbitrage in Prediction Markets] --> B{Key Methodology: Arbitrage Detection & Portfolio Optimization};
    B --> C[Data/Inputs: 1.9M Logical Relations, 255K Contracts, Polymarket Order Books];
    C --> D[Computational Processes: Convex Hull, Integer Programming, Order Book Replay];
    D --> E[Key Findings/Outcomes: 2.2% Guaranteed Profit, 3.2% Profit at Resolution, Arbitrage Persistence];

Cited References (18)

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  2. Equilibrium and welfare in markets with financially constrained arbitrageurs (2002) — link
  3. Low-Latency Trading (2011) — link
  4. Noise Trader Risk in Financial Markets (1990) — link
  5. The Cutting-Plane Method for Solving Convex Programs (1960) — link
  6. Anomalies: The Law of One Price in Financial Markets (2003) — link
  7. Geometric Algorithms and Combinatorial Optimization (1988) — link
  8. The Limits of Arbitrage (1995) — link
and 10 more
  1. How psychological framing affects economic market prices in the lab and field (2013) — link
  2. Complexity of combinatorial market makers (2008) — link
  3. Integer and Combinatorial Optimization (1988) — link
  4. Renting Balance Sheet Space: Intermediary Balance Sheet Rental Costs and the Valuation of Derivatives (2020) — link
  5. Costly arbitrage and the myth of idiosyncratic risk (2006) — link
  6. Hedge Funds: Past, Present, and Future (2007) — link
  7. Deviations from Covered Interest Rate Parity (2018) — link
  8. Asset Pricing and Sports Betting (2021) — link
  9. Complicated firms (2011) — link
  10. Prediction Markets (2004) — link

0 of 18 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.