On Arbitrage and Duality Under Model Uncertainty and Portfolio Constraints

20 Pages Posted: 13 Feb 2014  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Zhou Zhou

University of Minnesota - Twin Cities

Date Written: February 11, 2014

Abstract

We consider the fundamental theorem of asset pricing (FTAP) and hedging prices of options under non-dominated model uncertainty and portfolio constrains in discrete time. We first show that no arbitrage holds if and only if there exists some family of probability measures such that any admissible portfolio value process is a local super-martingale under these measures. We also get the non-dominated optional decomposition with constraints. From this decomposition, we get duality of the super-hedging prices of European options, as well as the sub- and super-hedging prices of American options. Finally, we get the FTAP and duality of super-hedging prices in a market where stocks are traded dynamically and options are traded statically.

Keywords: Fundamental theorem of asset pricing, sub-(super-)hedging, model uncertainty, portfolio constraints, optional decomposition

Suggested Citation

Bayraktar, Erhan and Zhou, Zhou, On Arbitrage and Duality Under Model Uncertainty and Portfolio Constraints (February 11, 2014). Available at SSRN: https://ssrn.com/abstract=2394190 or http://dx.doi.org/10.2139/ssrn.2394190

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

Zhou Zhou

University of Minnesota - Twin Cities ( email )

420 Delaware St. SE
Minneapolis, MN 55455
United States

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