Paper: arXiv 2503.14086

Authors: Alessandro Doldi, Marco Frittelli, Marco Maggis

Abstract

This paper builds on “Collective Arbitrage and the Value of Cooperation” by Biagini et al. (2025, forthcoming in “Finance and Stochastics”), which introduced in discrete time the notions of collective arbitrage and super-replication in a multi-agent market framework, where agents may operate in several submarkets and collaborate through risk exchange mechanisms. Expanding on these foundations, we establish a First Fundamental Theorem of Asset Pricing and a collective pricing-hedging duality under different assumptions and with new techniques compared to Biagini et al. (2025). We further introduce the notion of collective replication in order to study collective market completeness and provide a Second Fundamental Theorem of Asset Pricing in this cooperative multi-agent setting.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework extending the Fundamental Theorems of Asset Pricing and super-hedging duality to cooperative multi-agent segmented markets. It is purely theoretical with dense measure-theoretic probability and convex analysis, lacking empirical backtesting or real-world dataset applications.

Research Flowchart

  flowchart TD
    A[Research Goal: Extend Multi-Agent Market Framework to Collective Completeness & Pricing-Hedging Duality] --> B[Inputs: Discrete-time Submarket Structure & Risk Exchange Mechanisms]
    B --> C[Methodology: Formulate Collective Arbitrage & Replication Models]
    C --> D[Mathematical Derivations & Dual Optimization]
    D --> E[Outcome 1: First & Second Fundamental Theorems of Asset Pricing - FTAP]
    D --> F[Outcome 2: Characterization of Collective Market Completeness & Super-Replication Duality]

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1 of 82 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.