  We study time-consistency questions for processes of monetary risk measures
that depend on bounded discrete-time processes describing the evolution of
financial values. The time horizon can be finite or infinite. We call a process
of monetary risk measures time-consistent if it assigns to a process of
financial values the same risk irrespective of whether it is calculated
directly or in two steps backwards in time, and we show how this property
manifests itself in the corresponding process of acceptance sets. For processes
of coherent and convex monetary risk measures admitting a robust representation
with sigma-additive linear functionals, we give necessary and sufficient
conditions for time-consistency in terms of the representing functionals.
