Stochastic dominance constraints allow a decision maker to manage risk in an optimization
setting by requiring his or her decision to yield a random outcome which stochastically …

For many decision-making problems under uncertainty, it is crucial to develop risk-averse
models and specify the decision makers' risk preferences based on multiple stochastic …

For stochastic optimization problems with second order stochastic dominance constraints we
develop a new form of the duality theory featuring measures on the product of the probability …

This paper studies optimal path problems integrated with the concept of second order
stochastic dominance. These problems arise from applications where travelers are …

We consider two-stage risk-averse stochastic optimization problems with a stochastic
ordering constraint on the recourse function. Two new characterizations of the increasing …

LL-Almost Stochastic Dominance (LL-ASD) is a relaxation of the Stochastic Dominance (SD)
concept proposed by Leshno and Levy that explains more of realistic preferences observed …

This book offers a comprehensive presentation of the theory and methods of risk-averse
optimization and control. Problems of this type arise in finance, energy production and …

Stochastic dominance rules are well-characterized and widely used. This work aims to
describe and better understand the situations when they do not hold by developing …

The ability to compare random outcomes based on the decision makers' risk preferences is
crucial to modeling decision-making problems under uncertainty. In this tutorial, the primary …

We discuss main ideas of formalizing risk-averse preferences and using them in
optimization problems: utility theories, risk measures, and stochastic order constraints. We …