## 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
Full Text: