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Risks 2014, 2(4), 425-433; doi:10.3390/risks2040425

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

Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA
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Received: 13 May 2014 / Revised: 22 August 2014 / Accepted: 28 September 2014 / Published: 10 October 2014
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Abstract

We show that the recent results on the Fundamental Theorem of Asset Pricing and the super-hedging theorem in the context of model uncertainty 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. View Full-Text
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 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bayraktar, E.; Zhang, Y.; Zhou, Z. A Note on the Fundamental Theorem of Asset Pricing under Model Uncertainty. Risks 2014, 2, 425-433.

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