2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75248For 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.9 pagesFunctional Analysis46E30text