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Collective completeness and pricing-hedging duality II

Author

Listed:
  • Alessandro Doldi
  • Marco Frittelli
  • Marco Maggis

Abstract

This paper complements and extends Doldi, Frittelli and Maggis, Collective completeness and pricing-hedging duality, Math. Finan. Econ. 19, 757-784 (2025), by studying collective pricing and hedging when admissible risk exchanges form a finitely generated convex cone. The collective First Fundamental Theorem of Asset Pricing and the collective pricing-hedging duality are extended to this setting. A key contribution is a closedness result showing that no collective arbitrage implies the closedness of the aggregate feasibility cone combining infinite-dimensional trading opportunities with finite-dimensional exchanges. The paper also proves that no-collective-arbitrage prices for vectors of contingent claims form a relatively open convex set. Finally, strong collective replicability is introduced and shown to be equivalent to price uniqueness. This leads to an enhanced collective Second Fundamental Theorem of Asset Pricing, providing equivalent characterizations of collective completeness and strong collective completeness in terms of the uniqueness of the collective equivalent martingale measure. We highlight that several core aspects of the theory are substantially altered when exchanges belong to a convex cone rather than a vector space.

Suggested Citation

  • Alessandro Doldi & Marco Frittelli & Marco Maggis, 2026. "Collective completeness and pricing-hedging duality II," Papers 2606.19038, arXiv.org.
    • Handle: RePEc:arx:papers:2606.19038
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    References listed on IDEAS

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    3. Francesca Biagini & Alessandro Doldi & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2026. "Collective arbitrage and the value of cooperation," Finance and Stochastics, Springer, vol. 30(1), pages 1-57, January.
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    12. Carassus, Laurence, 2023. "No free lunch for markets with multiple numéraires," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    13. Alessandro Doldi & Marco Frittelli & Marco Maggis, 2025. "Collective completeness and pricing hedging duality," Papers 2503.14086, arXiv.org.
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