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Finance without probabilistic prior assumptions

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  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We develop the fundamental theorem of asset pricing in a probability- free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then endogenously as full support martingale measures (instead of equivalent martingale measures). A variant of the Harrison-Kreps-Theorem on viability and no arbitrage is shown. Finally, we show how to embed the superhedging problem in a classical infinite-dimensional linear programming problem.

Suggested Citation

  • Riedel, Frank, 2016. "Finance without probabilistic prior assumptions," Center for Mathematical Economics Working Papers 450, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:450
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    File URL: https://pub.uni-bielefeld.de/download/2900949/2900950
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    References listed on IDEAS

    as
    1. Joerg Vorbrink, 2010. "Financial markets with volatility uncertainty," Papers 1012.1535, arXiv.org, revised Dec 2010.
    2. Epstein, Larry G. & Ji, Shaolin, 2014. "Ambiguous volatility, possibility and utility in continuous time," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 269-282.
    3. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    4. Dieter Sondermann, 2006. "Introduction to Stochastic Calculus for Finance," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-34837-5, December.
    5. Bick, Avi & Willinger, Walter, 1994. "Dynamic spanning without probabilities," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 349-374, April.
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    Citations

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    Cited by:

    1. Gianluca Cassese, 2014. "Option Pricing in an Imperfect World," Papers 1406.0412, arXiv.org, revised Sep 2016.
    2. Alexander Alvarez & Sebastian Ferrando, 2014. "Trajectory Based Models, Arbitrage and Continuity," Papers 1403.5685, arXiv.org, revised Jan 2015.
    3. Marcel Nutz, 2014. "Superreplication under model uncertainty in discrete time," Finance and Stochastics, Springer, vol. 18(4), pages 791-803, October.
    4. Christopher W. Miller, 2016. "A Duality Result for Robust Optimization with Expectation Constraints," Papers 1610.01227, arXiv.org.
    5. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
    6. Romain Blanchard & Laurence Carassus, 2017. "Convergence of utility indifference prices to the superreplication price in a multiple-priors framework," Papers 1709.09465, arXiv.org, revised Oct 2020.
    7. Bruno Bouchard & Marcel Nutz, 2014. "Consistent Price Systems under Model Uncertainty," Papers 1408.5510, arXiv.org.
    8. Romain Blanchard & Laurence Carassus, 2021. "Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 366-398, January.

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    More about this item

    Keywords

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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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