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Weighted BMO and discrete time hedging within the Black-Scholes model
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  • Published: 09 October 2004

Weighted BMO and discrete time hedging within the Black-Scholes model

  • Stefan Geiss1 

Probability Theory and Related Fields volume 132, pages 39–73 (2005)Cite this article

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  • 12 Citations

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Abstract.

The paper combines two objects rather different at first glance: spaces of stochastic processes having weighted bounded mean oscillation (weighted BMO) and the approximation of certain stochastic integrals, driven by the geometric Brownian motion, by integrals over piece-wise constant integrands. The consideration of the approximation error with respect to weighted BMO implies L p and uniform distributional estimates for the approximation error by a John-Nirenberg type theorem. The general results about weighted BMO are given in the first part of the paper and applied to our approximation problem in the second one.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, 35 (MAD), 40014, Jyväskylä, Finland

    Stefan Geiss

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  1. Stefan Geiss
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Correspondence to Stefan Geiss.

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Cite this article

Geiss, S. Weighted BMO and discrete time hedging within the Black-Scholes model. Probab. Theory Relat. Fields 132, 39–73 (2005). https://doi.org/10.1007/s00440-004-0389-0

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  • Received: 02 November 2004

  • Revised: 21 May 2004

  • Published: 09 October 2004

  • Issue Date: May 2005

  • DOI: https://doi.org/10.1007/s00440-004-0389-0

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Keywords

  • Weighted BMO
  • John-Nirenberg theorem
  • Geometric Brownian motion
  • Stochastic integral
  • Quantitative approximation
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