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A Note on the Fundamental Theorem of Asset Pricing Under Model Uncertainty

Risks, 2(4), 425-433, 2014

9 Pages Posted: 17 Apr 2014 Last revised: 9 May 2015

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Yuchong Zhang

Columbia University

Zhou Zhou

University of Minnesota - Twin Cities

Date Written: August 21, 2014

Abstract

We show that the results of the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are non-redundant. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.

Keywords: Model uncertainty, bid-ask prices for options, semi-static hedging, non-dominated collection of probability measures, Fundamental Theorem of Asset Pricing, super-hedging, robust no-arbitrage, non-redundant options

Suggested Citation

Bayraktar, Erhan and Zhang, Yuchong and Zhou, Zhou, A Note on the Fundamental Theorem of Asset Pricing Under Model Uncertainty (August 21, 2014). Risks, 2(4), 425-433, 2014. Available at SSRN: https://ssrn.com/abstract=2425423 or http://dx.doi.org/10.2139/ssrn.2425423

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Yuchong Zhang

Columbia University ( email )

1255 Amsterdam Avenue
New York, NY 10027
United States

Zhou Zhou

University of Minnesota - Twin Cities ( email )

420 Delaware St. SE
Minneapolis, MN 55455
United States

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