  We define Conditional quasi concave Performance Measures (CPMs), on random
variables bounded from below, to accommodate for additional information. Our
notion encompasses a wide variety of cases, from conditional expected utility
and certainty equivalent to conditional acceptability indexes. We provide the
characterization of a CPM in terms of an induced family of conditional convex
risk measures. In the case of indexes these risk measures are coherent. Then,
Dynamic Performance Measures (DPMs) are introduced and the problem of time
consistency is addressed. The definition of time consistency chosen here
ensures that the positions which are considered good tomorrow are already
considered good today. We prove the equivalence between time consistency for a
DPM and weak acceptance consistency for the induced families of risk measures.
Finally, we extend CPMs and DPMs to dividend processes.
