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The wedge of arbitrage free prices: anything goes

Author

Listed:
  • Roko Aliprantis

    (Purdue University [West Lafayette])

  • Monique Florenzano

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Daniella Puzzello

    (Deparments of Economics and Mathematics - University of Kentucky - UK - University of Kentucky)

  • Rabee Tourky

    (Purdue University [West Lafayette], Department of Economics - University of Queensland - UQ [All campuses : Brisbane, Dutton Park Gatton, Herston, St Lucia and other locations] - The University of Queensland)

Abstract

We show that if K is a closed cone in a finite dimensional vector space X, then there exists a one-to-one linear operator T : X C [0,1] such that K is the pull-back cone of the positive cone of C [0,1], i.e., K = T -1 (C+ [0,1]). This problem originated from questions regarding arbitrage free prices in economics.

Suggested Citation

  • Roko Aliprantis & Monique Florenzano & Daniella Puzzello & Rabee Tourky, 2006. "The wedge of arbitrage free prices: anything goes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00112202, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00112202
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00112202
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    References listed on IDEAS

    as
    1. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2004. "General equilibrium analysis in ordered topological vector spaces," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 247-269, June.
    2. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2005. "Linear and non-linear price decentralization," Journal of Economic Theory, Elsevier, vol. 121(1), pages 51-74, March.
    3. N/A, 1970. "Note," Review of Radical Political Economics, Union for Radical Political Economics, vol. 2(4), pages 1-1, October.
    4. Aliprantis, C. D. & Florenzano, M. & Martins-da-Rocha, V. F. & Tourky, R., 2004. "Equilibrium analysis in financial markets with countably many securities," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 683-699, September.
    5. Aliprantis, Charalambos D. & Monteiro, Paulo K. & Tourky, Rabee, 2004. "Non-marketed options, non-existence of equilibria, and non-linear prices," Journal of Economic Theory, Elsevier, vol. 114(2), pages 345-357, February.
    6. Aliprantis, C. D. & Brown, D. J. & Polyrakis, I. A. & Werner, J., 1998. "Portfolio dominance and optimality in infinite security markets," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 347-366, October.
    7. repec:dau:papers:123456789/601 is not listed on IDEAS
    8. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    securities markets; arbitrage free prices; Closed cones; pull-back; marchés d'actifs; Cones fermés; images inverses de cones; prix sans arbitrage;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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