"Dynamic convex risk measures: time consistency, prudence, and sustainability" We study some properties of a dynamic convex risk measure for bounded random variables which describe terminal values of financial positions. In particular we characterize possible interdependence of conditional risk assessments at different times and the manifestation of these time consistency properties in dynamics of penalty functions and risk processes. In order to characterize investment processes we introduce the notion of sustainability, a property which means that the process can be upheld without risk. We show that sustainability can be characterized by a joint supermartingale property of the process and one-step penalty functions. The results will be illustrated in a financial market model with convex trading constraints.