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Fundamental Theorem of Asset Pricing Under Transaction Costs and Model Uncertainty

Forthcoming, Mathematics of Operations Research

24 Pages Posted: 8 Feb 2014 Last revised: 31 Aug 2015

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Yuchong Zhang

Columbia University

Date Written: September 5, 2013

Abstract

We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly non-dominated.

Using a backward-forward scheme, we show that when the market consists of a money market account and a single stock, no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. We also show that when the market consists of multiple dynamically traded assets and satisfies efficient friction, strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of strictly consistent price systems.

Keywords: Transaction costs, non-dominated collection of probability measures, Fundamental Theorem of Asset Pricing, martingale selection problem

Suggested Citation

Bayraktar, Erhan and Zhang, Yuchong, Fundamental Theorem of Asset Pricing Under Transaction Costs and Model Uncertainty (September 5, 2013). Forthcoming, Mathematics of Operations Research. Available at SSRN: https://ssrn.com/abstract=2392001 or http://dx.doi.org/10.2139/ssrn.2392001

Erhan Bayraktar

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 (Contact Author)

Columbia University ( email )

1255 Amsterdam Avenue
New York, NY 10027
United States

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