  Monitoring means to observe a system for any changes which may occur over
time, using a monitor or measuring device of some sort. In this paper we
formulate a problem of monitoring dates of maximal risk of a financial
position. Thus, the systems we are going to observe arise from situations in
finance. The measuring device we are going to use is a time-consistent measure
of risk.
  In the first part of the paper we discuss the numerical representation of
conditional convex risk measures which are defined in a space Lp(F,R) and take
values in L1(G,R). This will allow us to consider time-consistent convex risk
measures in L1(R).
  In the second part of the paper we use a time-consistent convex risk measure
in order to define an abstract problem of monitoring stopping times of maximal
risk. The penalty function involved in the robust representation changes
qualitatively the time when maximal risk is for the first time identified. A
phenomenon which we discuss from the point of view of robust statistics.
