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...

We discuss how the standard Cost-Benefit Analysis should be modified in order to take risk (and uncertainty) into account. We propose different approaches used in finance (Value at Risk, Conditional Value at Risk, Downside Risk Measures, and Efficiency Ratio) as useful tools to model the impact...

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...

We consider the problem of estimating regression models of two-dimensional random fields. Asymptotic properties of the least squares estimator of the linear regression coefficients are studied for the case where the disturbance is a homogeneous random field with an absolutely continuous spectral...

Transverse spiral (i.e., pure twist) director configurations occur when cholesteric liquid crystals are confined between two parallel plates such that the director is strongly anchored in fixed directions in the film plane at the boundaries. Such states, however, are no longer stable when the...