  We study topological and metric properties of the so-called interval
translation maps (ITMs). For these maps, we introduce the maximal invariant
measure and demonstrate that an ITM, endowed with such a measure, is metrically
conjugated to an interval exchange map (IEM). This allows us to extend some
properties of IEMs (e.g. an estimate of the number of ergodic measures and the
minimality of the symbolic model) to ITMs. Further, we prove a version of the
closing lemma and study how the invariant measures depend on parameters of the
system. These results are illustrated by a simple example or a risk management
model where interval translation maps appear naturally.
