Finance without Probabilistic Prior Assumptions
AbstractWe 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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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 450.
Length: 18 pages
Date of creation: Jun 2011
Date of revision:
Probability-Free Finance; Fundamental Theorem of Asset Pricing; Full-Support Martingale Measure; Superhedging; Infinite-Dimensional Linear Programming;
Other versions of 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-07-02 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Bick, Avi & Willinger, Walter, 1994. "Dynamic spanning without probabilities," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 349-374, April.
- Larry Epstein & Shaolin Ji, 2011. "Ambiguous Volatility, Possibility and Utility in Continuous Time," Papers 1103.1652, arXiv.org, revised Jan 2013.
- Marcel Nutz, 2013. "Superreplication under Model Uncertainty in Discrete Time," Papers 1301.3227, arXiv.org, revised Feb 2014.
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