Appears in collection : Innovative Research in Mathematical Finance / Recherche innovante en mathématiques financières

Non-convex random sets of admissible positions naturally arise in the setting of fixed transaction costs or when only a finite range of possible transactions is considered. The talk defines set-valued risk measures in such cases and explores the situations when they return convex result, namely, when Lyapunov's theorem applies. The case of fixed transaction costs is analysed in greater details. Joint work with Andreas Haier (FINMA, Switzerland).