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Separation of a super- and a submartingale by a martingale. (Séparation d’une sur- et d’une sousmartingale par une martingale.) (French) Zbl 0912.60065

Azéma, Jacques (ed.) et al., Séminaire de probabilités XXXII. Berlin: Springer. Lect. Notes Math. 1686, 67-72 (1998).
E. Jouini and H. Kallal [J. Econ. Theory 54, 259-304 (1995)] have shown that if \(X\) is a supermartingale and \(Y\) a submartingale such that \(X\leq Y\), then there exists a martingale \(M\) such that \(X\leq M\leq Y\). This result was motivated by the study of security markets in mathematical finance. The note under review provides the following refinement: \(M\) can be chosen in the form \(M=X +\lambda(Y-X)\) where \(\lambda\) is a predictable process with values in \([0,1]\).
For the entire collection see [Zbl 0893.00035].
Reviewer: J.Bertoin (Paris)

MSC:

60G44 Martingales with continuous parameter
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