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December 2016 Arbitrage, hedging and utility maximization using semi-static trading strategies with American options
Erhan Bayraktar, Zhou Zhou
Ann. Appl. Probab. 26(6): 3531-3558 (December 2016). DOI: 10.1214/16-AAP1184

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.

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Erhan Bayraktar. Zhou Zhou. "Arbitrage, hedging and utility maximization using semi-static trading strategies with American options." Ann. Appl. Probab. 26 (6) 3531 - 3558, December 2016. https://doi.org/10.1214/16-AAP1184

Information

Received: 1 July 2015; Revised: 1 December 2015; Published: December 2016
First available in Project Euclid: 15 December 2016

zbMATH: 1357.91046
MathSciNet: MR3582810
Digital Object Identifier: 10.1214/16-AAP1184

Subjects:
Primary: 49L20, 60G40, 60G42, 91G20, 93E20

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 6 • December 2016
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