Collective Free Lunch and the FTAP
Frittelli’s paper extends collective arbitrage theory to general semimartingale markets, deriving a Fundamental Theorem of Asset Pricing and pricing-hedging duality.
What it examines
This paper extends earlier work on collective arbitrage to a broader semimartingale market model, introducing the novel concept of a collective free lunch. It derives collective versions of the Fundamental Theorem of Asset Pricing and pricing-hedging duality, enhancing our understanding of market segmentation and collective risk management.
What it concludes
The results connect the absence of collective free lunch with equivalent martingale measures, advancing pricing and hedging in segmented markets. This work aids risk management and cooperative trading strategies, suggesting future research may relax assumptions to further broaden its practical applications.
Evidence objects
Researchers extend arbitrage and free lunch concepts from discrete markets to a semimartingale framework by introducing the novel $$\text{Collective Free Lunch}$$, establishing that $$NCFL(Y)$$ implies an equivalent separating probability measures.
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The study pioneers innovative definitions for risk exchange among segmented agents, establishes a collective pricing-hedging duality and multi-dimensional Kreps-Yan theorem, revealing hidden arbitrage opportunities through cooperation despite individual no-arbitrage conditions.
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Using advanced techniques such as convex duality, Fatou closure, and weak star topologies, the study offers rigorous proofs amid technical boundedness assumptions, bolstering insights into arbitrage, pricing, and risk management.
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Extending established quantitative finance theories, the paper introduces the innovative $$\text{Collective Free Lunch}$$ concept within a general semimartingale market framework. It develops a collective version of the Fundamental Theorem of Asset Pricing and pricing-hedging duality, offering novel risk management insights. Its broad market implications render it compelling and uniquely significant.
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Raw abstract and provenance
- This paper extends the analysis presented in [Biagini et al., Collective Arbitrage and the Value of Cooperation, forthcoming on Finance Stoch. 2025 (arXiv:2306.11599v2, …
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