Uncertainty pervades most aspects of life. From selecting a new technology to choosing a career, decision makers rarely know in advance the exact outcomes of their decisions. Whereas the consequences of decisions in standard decision theory are explicitly described (the decision from description...

We provide an economic interpretation of the practice consisting in incorporating risk measures as constraints in a classic expected return maximization problem. For what we call the infimum of expectations class of risk measures, we show that if the decision maker (DM) maximizes the expectation...

We study optimization problems subject to possible fatal failures. The probability of failure should not exceed a given confidence level. The distribution of the failure event is assumed unknown, but it can be generated via simulation or observation of historical data. Gradient-based...