------------------------------------------------------------------------ University of Vienna, Faculty of Mathematics ------------------------------------------------------------------------ Tu., 20.05.2014, 17:00, seminar room 10 Uni Wien, 1090 Wien, Oskar-Morgenstern-Platz 1, 2nd floor José Miguel Zapata (Univ. of Murcia & BBVA asset management, Spain) http://es.linkedin.com/pub/jose-miguel-zapata/28/46a/578 "Locally L^0-convex modules and conditional risk measures" Abstract: Locally L^0-convex modules are thought to be the suitable analytic foundation for conditional risk measures. With respect this idea, we review the notion of locally L^0-convex topologies and provide a characterization theorem of locally L^0-convex topologies induced by a family of L^0-seminorms, giving a counterexample of a locally L^0-convex topology which cannot be induced by any family of L^0-seminorms. We also review some important results drawn from convex analysis and adapted to L^0-modules: hyperplane separation theorems for L^0-modules as well as continuity, subdifferentiability and a dual representation of Fenchel-Moreau type for L^0-convex functions from L^0-modules into L^0. ------------------------------------------------------------------------