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A note on lower bounds of martingale measure densities

Dmitry Rokhlin·Walter Schachermayer
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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.

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Dmitry Rokhlin, Walter Schachermayer. 2005-05-19. A note on lower bounds of martingale measure densities. https://arxiv.org/abs/math/0505411

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