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...

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...

When dealing with numerical solution of stochastic optimal control problems, stochastic dynamic programming is the natural framework. In order to try to overcome the so-called curse of dimensionality, the stochastic programming school promoted another approach based on scenario trees which can...