Geodesic
A Note on Martingale Measures with Bounded Densities
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 212-216 
M. Rásonyi. A Note on Martingale Measures with Bounded Densities. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic financial mathematics, Tome 237 (2002), pp. 212-216. http://geodesic.mathdoc.fr/item/TM_2002_237_a10/
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     title = {A~Note on {Martingale} {Measures} with {Bounded} {Densities}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $S$ be a discrete-time martingale with a finite horizon. We show that the set of equivalent martingale measures with bounded densities is dense in the set of equivalent martingale measures with respect to the total variation norm.

[1] Dellacherie C., Meyer P. A., Probabilities and potential, North-Holland, Amsterdam, 1978 | MR | Zbl

[2] Dalang R. C., Morton A., Willinger W., “Equivalent martingale measures and no-arbitrage in stochastic securities market models”, Stoch. and Stoch. Repts., 29 (1990), 185–201 | MR | Zbl

[3] Hiriart-Urruty J.-B., Lemaréchal C., Convex analysis and minimization algorithms, Pt 1: Fundamentals, Springer-Verl., Berlin, Heidelberg, New York, 1996 | MR

[4] Kabanov Yu. M., Stricker Ch., “On equivalent martingale measures with bounded densities”, Séminaire de probabilités, XXXV, Lect. Notes Math., 1755, eds. J. Azéma et al., Springer-Verl., Berlin, 2001, 139–148 | MR | Zbl