Multi-period decision making in finance: time consistency versus information monotonicity

We consider stochastic financial optimization multi-period decision problems. Many risk functionals have been proposed and discussed recently for modeling the risk in such problems. One often required property is “time-consistency”, which—loosely spoken—is the property that decision plans being optimal at time $t$ should remain optimal at time $t+1$ and later. Nested risk functionals lead to time consistency. On the other hand, an also very reasonable requirement is that acceptable decisions remain acceptable if more information is available, i.e. a monotonicity property w.r.t. information expressed in term of filtrations. However information monotonicity contradicts in a certain way time consistency, such that only nearly trivial risk functionals have both properties.