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A remark on the set of arbitrage-free prices in a multi-period model

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  • Bernard Cornet
  • Abhishek Ranjan

Abstract

We study the convexity property of the set Q[subscript F] of arbitrage-free prices of a multi-period financial structure F. The set of arbitrage-free prices is shown to be a convex cone under conditions on the financial structure F that hold in particular for short-lived assets. Furthermore, we provide examples of equivalent financial structures F and F' such that Q[subscript F] is a convex cone, but Q[subscript F'] is neither convex nor a cone.
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  • Bernard Cornet & Abhishek Ranjan, 2013. "A remark on the set of arbitrage-free prices in a multi-period model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 35-43, March.
    • Handle: RePEc:bla:ijethy:v:9:y:2013:i:1:p:35-43
    DOI: 10.1111/j.1742-7363.2013.12004.x
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    References listed on IDEAS

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    1. Aouani, Zaier & Cornet, Bernard, 2011. "Reduced equivalent form of a financial structure," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 318-327.
    2. Aouani, Zaier & Cornet, Bernard, 2009. "Existence of financial equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 772-786, December.
    3. Florenzano, Monique & Gourdel, Pascal, 1994. "T-period economies with incomplete markets," Economics Letters, Elsevier, vol. 44(1-2), pages 91-97.
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    1. Bernard Cornet & Abhishek Ranjan, 2013. "Equilibria in a multi-period economy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801402, HAL.
    2. Jean-Marc Bonnisseau & Achis Chery, 2018. "Stability of marketable payoffs with re-trading," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01896592, HAL.
    3. Alain Chateauneuf & Bernard Cornet, 2022. "Submodular financial markets with frictions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 721-744, April.

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