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Mathematical Methods of Operations Research

, Volume 87, Issue 2, pp 197–227 | Cite as

Quantile Hedging in a semi-static market with model uncertainty

  • Erhan Bayraktar
  • Gu Wang
Original Article
  • 172 Downloads

Abstract

With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the agent 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 helps numerical calculation of the quantile hedging price. As the discretization becomes finer, the approximate quantile hedging price converges and the hedging strategy is asymptotically optimal in the original market.

Keywords

Quantile hedging Model uncertainty Semi-static hedging Neyman–Pearson Lemma 

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Department of Mathematical SciencesWorcester Polytechnic InstituteWorcesterUSA

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