This is an announcement for the paper "A note on lower bounds of martingale measure densities" by D. Rokhlin and W. Schachermayer.

Abstract: For a given element $f\in L^1$ and a convex cone $C\subset L^\infty$, $C\cap L^\infty_+={0}$ we give necessary and sufficient conditions for the existence of an element $g\ge f$ lying in the polar of $C$. This polar is taken in $(L^\infty)^*$ and in $L^1$. In the context of mathematical finance the main result concerns the existence of martingale measures, whose densities are bounded from below by prescribed random variable.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46E30

Remarks: 9 pages

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Submitted from: rokhlin@math.rsu.ru

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