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<p>This paper builds on <i>Collective Arbitrage and the Value of Cooperation</i> by Biagini et al. (2025, forthcoming in <i>Finance and Stochastics</i>), 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.</p>

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Collective completeness and pricing hedging duality

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Alessandro Doldi,
  • Marco Frittelli,
  • Marco Maggis

摘要

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.