Time-consistency of risk measures: how strong is such a property?
Emanuela Rosazza (University of Milano Bicocca) gives a lecture with a title: Time-consistency of risk measures: how strong is such a property?
Quite recently, a great interest has been devoted to time-consistency of risk measures in its different formulations (see Delbaen (2006), Foellmer and Penner (2006), Bion-Nadal (2008), Delbaen, Peng and Rosazza Gianin (2010), Laeven and Stadje (2014), among many others). However, almost all the papers address to coherent or convex risk measures satisfying cash-invariance.
In the present work we study time-consistency for more general dynamic risk measures where either only cash-invariance or both cash-invariance and convexity are dropped. This analysis is motivated by the recent papers of El Karoui and Ravanelli (2009) and Cerreia-Vioglio, Maccheroni, Marinacci and Montrucchio (2011) who discussed and weakened the axioms above by introducing cash-subadditivity and quasiconvexity. In particular, we investigate and discuss if the notion of time consistency is too restrictive, when considered in the general framework of quasiconvex and cash-subadditive risk measures and, consequently, leads to a very special class of risk measures. Finally, we provide some conditions guaranteeing time-consistency in this more general framework.
This is based on a joint work with Elisa Mastrogiacomo.