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Quantile Hedging in a Semi-Static Market with Model Uncertainty

28 Pages Posted: 21 Aug 2014 Last revised: 25 Sep 2017

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Gu Wang

Worcester Polytechnic Institute

Date Written: July 15, 2015

Abstract

With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the investor minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality results which link quantile hedging to a randomized composite hypothesis test, an arbitrage-free discretization of the market is proposed as an approximation. The discretized market has a dominating measure, which guarantees the existence of the optimal hedging strategy and enables numerical calculation of the quantile hedging price by applying the generalized Neyman-Pearson Lemma. Finally, the performance in the original market of the approximating hedging strategy and the convergence of the approximating quantile hedging price are analyzed.

Keywords: Quantile hedging, Model Uncertainty, Semi-static Hedging, Neyman-Pearson Lemma

JEL Classification: G11, G12, G13, D81

Suggested Citation

Bayraktar, Erhan and Wang, Gu, Quantile Hedging in a Semi-Static Market with Model Uncertainty (July 15, 2015). Available at SSRN: https://ssrn.com/abstract=2483880 or http://dx.doi.org/10.2139/ssrn.2483880

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

Gu Wang (Contact Author)

Worcester Polytechnic Institute ( email )

100 Institute Road
Worcester, MA 01609
United States

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