Asymptotically Stable Dynamic Risk Assessments

In this paper asymptotically stable risk assessments are studied. They are characterized by not being sensitive with respect to huge additional capital in the very far future. Under the additional hypothesis of being locally continuous from below, these risk assessments are exactly those which allow a robust representation with so-called local test probabilities having a support with finite time horizon.Time-consistent risk assessments can be constructed by composing a sequence of generators. We give several conditions for the generators such that the resulting risk assessments are indeed asymptotically stable