Optional decomposition and Lagrange multipliers

H. Föllmer and Y.M. Kabanov
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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
Authors registered in the RePEc Author Service: Юрий Михайлович Кабанов

Finance and Stochastics, 1997, vol. 2, issue 1, 69-81

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.

Keywords: Optional decomposition; semimartingale; equivalent martingale measure; Hellinger process; Lagrange multiplier (search for similar items in EconPapers)
JEL-codes: G10 G12 (search for similar items in EconPapers)
Date: 1997-11-13
Note: received: January 1996; final version received: June 1997
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Citations: View citations in EconPapers (11)

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