Optional Decomposition and Lagrange Multipliers

Finance and Stochastics, Vol 2 No 1, 1998

Posted: 21 Apr 1998

See all articles by Hans Föllmer

Hans Föllmer

Humboldt University of Berlin

Youri Kabanov

Universite de Franche-Comte; Russian Academy of Sciences (RAS) - Central Economics and Mathematics Institute

Abstract

Let 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 Q. The optional decomposition theorem for X states that there exists a predictable integrand phi such that the difference X-phi times 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.

JEL Classification: G10, G12

Suggested Citation

Follmer, Hans and Kabanov, Youri, Optional Decomposition and Lagrange Multipliers. Finance and Stochastics, Vol 2 No 1, 1998, Available at SSRN: https://ssrn.com/abstract=78448

Hans Follmer (Contact Author)

Humboldt University of Berlin ( email )

Unter den Linden 6
Berlin, D-10099
Germany
49 30 2093 5817 (Phone)
49 30 2093 5848 (Fax)

Youri Kabanov

Universite de Franche-Comte ( email )

16 Route de Gray
Besancon Cedex, F-25030
France

Russian Academy of Sciences (RAS) - Central Economics and Mathematics Institute

47, Nakhimovsky prospect
Moscow, 117418
Russia

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