Tight Approximations of Dynamic Risk Measures

There are two natural ways to measure risk across many periods: apply a single risk measure to the total future cost, or compose one-step risk mappings. We characterize when one always dominates the other and introduce a metric for how far apart they are. An asymmetry emerges — the tightest upper bound admits an exact characterization, while the lower bound does not.

Mathematics of Operations Research, vol. 40, no. 3, pp. 655–682