Update rules for convex risk measures

Abstract

In the first part of the paper we investigate properties that describe the intertemporal structure of dynamic convex risk measures. The usual backward approach to dynamic risk assessment leads to strong and weak versions of time consistency. As an alternative, we introduce a forward approach of consecutivity.

In the second part we discuss the problem of how to update a convex risk measure when new information arrives. We analyse to what extent the above properties are appropriate update criteria.