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Finance Without Probabilistic Prior Assumptions

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  • Frank Riedel

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.

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  • Frank Riedel, 2011. "Finance Without Probabilistic Prior Assumptions," Papers 1107.1078, arXiv.org.
    • Handle: RePEc:arx:papers:1107.1078
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    References listed on IDEAS

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    1. 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.
    2. Bick, Avi & Willinger, Walter, 1994. "Dynamic spanning without probabilities," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 349-374, April.
    3. Joerg Vorbrink, 2010. "Financial markets with volatility uncertainty," Papers 1012.1535, arXiv.org, revised Dec 2010.
    4. 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.
    5. Dieter Sondermann, 2006. "Introduction to Stochastic Calculus for Finance," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-34837-5, October.
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    Cited by:

    1. Alexander Alvarez & Sebastian Ferrando, 2014. "Trajectory Based Models, Arbitrage and Continuity," Papers 1403.5685, arXiv.org, revised Jan 2015.
    2. Christopher W. Miller, 2016. "A Duality Result for Robust Optimization with Expectation Constraints," Papers 1610.01227, arXiv.org.
    3. Marcel Nutz, 2014. "Superreplication under model uncertainty in discrete time," Finance and Stochastics, Springer, vol. 18(4), pages 791-803, October.
    4. Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
    5. 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.
    6. Gianluca Cassese, 2014. "Option Pricing in an Imperfect World," Papers 1406.0412, arXiv.org, revised Sep 2016.
    7. 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.
    8. Bruno Bouchard & Marcel Nutz, 2014. "Consistent Price Systems under Model Uncertainty," Papers 1408.5510, arXiv.org.

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    More about this item

    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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