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Arbitrage, Hedging and Utility Maximization Using Semi-Static Trading Strategies with American Options

14 Pages Posted: 26 Feb 2015 Last revised: 27 Feb 2015

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Zhou Zhou

University of Minnesota - Twin Cities

Date Written: February 26, 2015

Abstract

We consider a financial model where stocks are available for dynamic trading, and European and American options are available for static trading (semi-static trading strategies). We assume that the American options are infinitely divisible, and can only be bought but not sold. We first get the fundamental theorem of asset pricing (FTAP) using semi-static trading strategies. Using the FTAP result, we further get the dualities for the hedging prices of European and American options. Based on the hedging dualities, we also get the duality for the utility maximization involving semi-static trading strategies.

Keywords: Fundamental theorem of asset pricing, hedging duality, utility maximization, semi-static trading strategies, American options

Suggested Citation

Bayraktar, Erhan and Zhou, Zhou, Arbitrage, Hedging and Utility Maximization Using Semi-Static Trading Strategies with American Options (February 26, 2015). Available at SSRN: https://ssrn.com/abstract=2569256 or http://dx.doi.org/10.2139/ssrn.2569256

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

Zhou Zhou (Contact Author)

University of Minnesota - Twin Cities ( email )

420 Delaware St. SE
Minneapolis, MN 55455
United States

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