×

Optional decomposition and Lagrange multipliers. (English) Zbl 0894.90016

Summary: Let \({\mathcal Q}\) 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 \({\mathcal Q}\). 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.

MSC:

91B28 Finance etc. (MSC2000)
60H05 Stochastic integrals
PDF BibTeX XML Cite
Full Text: DOI Link