Illinois Journal of Mathematics

A note on lower bounds of martingale measure densities

Dmitry Rokhlin and Walter Schachermayer

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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 a prescribed random variable.

Article information

Illinois J. Math., Volume 50, Number 1-4 (2006), 815-824.

First available in Project Euclid: 12 November 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G44: Martingales with continuous parameter
Secondary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]


Rokhlin, Dmitry; Schachermayer, Walter. A note on lower bounds of martingale measure densities. Illinois J. Math. 50 (2006), no. 1-4, 815--824. doi:10.1215/ijm/1258059493.

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