Risk averse stochastic programming: time consistency and optimal stopping

Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically or time consistent and introduces stopping time risk measures. It turns out that the paradigm of time consistency is in conflict with various desirable, classical properties of general risk measures.