  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.
