Coherent multiperiod risk adjusted values and Bellman's principle

Starting with a time-0 coherent risk measure defined for value processes, we also define risk measurement processes. Two other constructions of measurement processes are given in terms of sets of test probabilities. These latter constructions are identical and are related to the former construction when the sets fulfill a stability condition also met in multi-period treatment of ambiguity as in decision-making. We finally deduce risk measurements for the final value of locked-in positions and repeat a warning concerning Tail-Value-at-Risk.