A note on lower bounds of martingale measure densities

Rokhlin, Dmitry; Schachermayer, Walter

Illinois J. Math., Tome 50 (2006) no. 1-4, p. 815-824 / Harvested from Project Euclid

Résumé

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.

Publié le : 2006-05-15
Classification: 60G44, 60J45

@article{1258059493,
     author = {Rokhlin, Dmitry and Schachermayer, Walter},
     title = {A note on lower bounds of martingale measure densities},
     journal = {Illinois J. Math.},
     volume = {50},
     number = {1-4},
     year = {2006},
     pages = { 815-824},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258059493}
}

Rokhlin, Dmitry; Schachermayer, Walter. A note on lower bounds of martingale measure densities. Illinois J. Math., Tome 50 (2006) no. 1-4, pp.  815-824. http://gdmltest.u-ga.fr/item/1258059493/