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 worst cases, whereas classical methods quantify risk in terms of probabilities. The 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.
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