The Annals of Applied Probability

Arbitrage, hedging and utility maximization using semi-static trading strategies with American options

Erhan Bayraktar and Zhou Zhou

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We consider a financial market 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. In the first part of the paper, we work within the framework without model ambiguity. We first get the fundamental theorem of asset pricing (FTAP). Using the FTAP, we 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. In the second part of the paper, we consider the market which admits nondominated model uncertainty. We first establish the hedging result, and then using the hedging duality we further get the FTAP. Due to the technical difficulty stemming from the nondominancy of the probability measure set, we use a discretization technique and apply the minimax theorem.

Article information

Ann. Appl. Probab., Volume 26, Number 6 (2016), 3531-3558.

Received: July 2015
Revised: December 2015
First available in Project Euclid: 15 December 2016

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Zentralblatt MATH identifier

Primary: 60G42: Martingales with discrete parameter 91G20: Derivative securities 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 49L20: Dynamic programming method 93E20: Optimal stochastic control

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


Bayraktar, Erhan; Zhou, Zhou. Arbitrage, hedging and utility maximization using semi-static trading strategies with American options. Ann. Appl. Probab. 26 (2016), no. 6, 3531--3558. doi:10.1214/16-AAP1184.

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