Stochastic orders formalize preferences among random outcomes. They are widely for comparing random outcomes in statistics and economics. In this talk, we discuss optimization problems involving stochastic-order relations as constraints that relate decision-dependent performance functionals to benchmark random outcomes.

We discuss the relation of stochastic orderings to utility functions and to coherent measures of risk. Necessary and sufficient conditions of optimality and duality theory for problems with stochastic order constraints involve expected utility theory, dual (rank-dependent) utility theory, and coherent measures of risk. The model provides a link between various approaches to risk-averse optimization. The discussion will include a comparison of random sequences in the context of multistage stochastic optimization problems. The framework enables the design of time-consistent optimal policy, ensuring stochastic dominance over a sequential benchmark. Throughout the talk, special attention will be paid to optimal portfolio design.

Bio: Darinka Dentcheva is a professor at the Department of Mathematical Sciences at the Stevens Institute of Technology, where she held the position of the Chair of the Department and the Chair of the Faculty Senate at Stevens Institute. She has a PhD degree and a Habilitation both conferred by Humboldt University Berlin, Germany. Her research interests are in the area of theory and methods of optimization under uncertainty and risk, statistical learning, and their application to mathematical finance, insurance, robotics, energy production and distribution, medicine, and others. She has acquired broad experience in research and teaching during her career in the United States, Germany, and Bulgaria. Dentcheva is passionate about education and has created several curricula and multiple courses at the graduate and undergraduate level. In recognition of her research achievements, she has given plenary talks at major international conferences in Vienna (Austria), Paris (France), Sofia (Bulgaria), Berlin (Germany), Santiago (Chile), Venice (Italy), and others. She has served the scientific community in a variety of roles such as associate editor of seven international journals, including SIAM Journal on Optimization (for 16 years), and SIAM Review (for 15 years), as a member of the committee on Stochastic programming, the publication committee of MOS, the SIAM Journal committee, and other international bodies.