In this paper, we investigate two different frameworks for assessing the risk
in a multi-period decision process: a dynamically inconsistent formulation
(whereby a single, static risk measure is applied to the entire sequence of
future costs), and a dynamically consistent one, obtained by suitably composing
one-step risk mappings. We characterize the class of dynamically consistent
measures that provide a tight approximation for a given inconsistent measure,
and discuss how the approximation factors can be computed.