Collective Arbitrage and the Value of Cooperation

Paper: arXiv 2306.11599

Authors: Francesca Biagini, Alessandro Doldi, Jean-Pierre Fouque, Marco Frittelli, Thilo Meyer-Brandis

Abstract

We introduce the notions of Collective Arbitrage and of Collective Super-replication in a discrete-time setting where agents are investing in their markets and are allowed to cooperate through exchanges. We accordingly establish versions of the fundamental theorem of asset pricing and of the pricing-hedging duality. A reduction of the price interval of the contingent claims can be obtained by applying the collective super-replication price.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a strong theoretical framework extending classic mathematical finance concepts (FTAP and super-replication) to multi-agent cooperative settings using rigorous discrete-time measure theory. However, it lacks empirical validation, backtesting, or real-world data analysis, remaining strictly theoretical.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate Market Cooperation via Collective Arbitrage & Super-replication] --> B[Input: Discrete-Time Market Models & Contingent Claims]
    B --> C[Formulate Cooperation Rules & Exchange Mechanisms]
    C --> D[Establish Collective FTAP & Pricing-Hedging Duality]
    D --> E[Compute Collective Super-Replication Prices]
    E --> F[Outcome: Reduced Price Interval for Contingent Claims]