  We develop a risk-averse safety analysis method for stochastic systems on
discrete infinite time horizons. Our method quantifies the notion of risk for a
control system in terms of the severity of a harmful random outcome in a
fraction of the worst cases. In contrast, classical methods quantify risk in
terms of the probability of a harmful event. Our theoretical arguments are
based on the analysis of a value iteration algorithm on an augmented state
space. We provide conditions to guarantee the existence of an optimal policy on
this space. We illustrate the method numerically using an example from the
domain of stormwater management.
