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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1481792592

Digital Object Identifier
doi:10.1214/16-AAP1184

Mathematical Reviews number (MathSciNet)
MR3582810

Zentralblatt MATH identifier
1357.91046

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1481792592


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