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Optional decomposition and Lagrange multipliers

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Author Info

  • H. Föllmer

    (Institut für Mathematik, Humboldt Universität, Unter den Linden 6, D-10099 Berlin, Germany)

  • Y.M. Kabanov

    (Central Economics and Mathematics Institute of the Russian Academy of Sciences, Moscow)

Abstract

Let ${\cal Q}$ be the set of equivalent martingale measures for a given process $S$, and let $X$ be a process which is a local supermartingale with respect to any measure in ${\cal Q}$. The optional decomposition theorem for $X$ states that there exists a predictable integrand $\varphi$ such that the difference $X-\varphi\cdot S$ is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption.

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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 2 (1997)
Issue (Month): 1 ()
Pages: 69-81

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Handle: RePEc:spr:finsto:v:2:y:1997:i:1:p:69-81

Note: received: January 1996; final version received: June 1997
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Related research

Keywords: Optional decomposition; semimartingale; equivalent martingale measure; Hellinger process; Lagrange multiplier;

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Cited by:
  1. Peter Bank & Frank Riedel, 1999. "Optimal Consumption Choice under Uncertainty with Intertemporal Substitution," GE, Growth, Math methods 9908002, EconWPA.
  2. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
  3. Filipovic, Damir & Kupper, Michael, 2007. "Monotone and cash-invariant convex functions and hulls," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 1-16, July.
  4. Frank Riedel, 2007. "Optimal stopping under ambiguity," Working Papers 390, Bielefeld University, Center for Mathematical Economics.
  5. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.
  6. Matos, Joao Amaro de & Lacerda, Ana, 2004. "Dry Markets and Superreplication Bounds of American Derivatives," FEUNL Working Paper Series wp461, Universidade Nova de Lisboa, Faculdade de Economia.

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