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Optional decompositions under constraints
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  • Published: September 1997

Optional decompositions under constraints

  • H. Föllmer1 &
  • D. Kramkov2 

Probability Theory and Related Fields volume 109, pages 1–25 (1997)Cite this article

Summary.

Motivated by a hedging problem in mathematical finance, El Karoui and Quenez [7] and Kramkov [14] have developed optional versions of the Doob-Meyer decomposition which hold simultaneously for all equivalent martingale measures. We investigate the general structure of such optional decompositions, both in additive and in multiplicative form, and under constraints corresponding to different classes of equivalent measures. As an application, we extend results of Karatzas and Cvitanić [3] on hedging problems with constrained portfolios.

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Authors and Affiliations

  1. Humboldt-Universität zu Berlin, Institut für Mathematik, Unter den Linden 6, D-10099 Berlin, , , , ,

    H. Föllmer

  2. Steklov Mathematical Institute, Gubkina 8, GSP-1, 117966, Moscow, Russia, , , , , , RU

    D. Kramkov

Authors
  1. H. Föllmer
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  2. D. Kramkov
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Received: 6 August 1996/In revised form: 5 March 1997

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Föllmer, H., Kramkov, D. Optional decompositions under constraints. Probab Theory Relat Fields 109, 1–25 (1997). https://doi.org/10.1007/s004400050122

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  • Issue Date: September 1997

  • DOI: https://doi.org/10.1007/s004400050122

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  • Mathematics Subject Classification (1991): 60G44
  • 60H05
  • 60H30
  • 90A09
  • 93E20
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