6 julio, 2020
12:00

Título: On the Stochastic Dominance functional-basedrisk averse versions in mathematical optimization under uncertainty

Ponente: Laureano F. Escudero, Universidad Rey Juan Carlos, Móstoles (Madrid)

Organizador: Juan Francisco Monge Ivars

Fecha: Lunes 6 de julio de 2020 a las 12:00 horas.

Lugar:  Online (Se os facilitara aquí el link el mismo día 30 minutos antes de la charla para que podáis acceder)

meet.google.com/aje-wpzm-nfh

Abstract: Frequently, mainly in dynamic problems,some data is uncertain at the decision-making time, although some informationis already available. The mathematical optimizationmodels under uncertainty, so-named stochastic optimization ones structurethe uncertainty in a set of representative scenarios. The stochastic RiskNeutral (RN) models aim to obtaining a feasible solution for the scenario-basedconstraint system that, say, maximizes the expected objective function value inthe scenarios. The RN approach has been used since the 60s. The good news is that,even within the difficulty of solving realistic stochastic models mainly in thepresence of integer variables, the nice structure of the two-stage andmultistage models can be exploited in problem solving. However, that approach means that the optimal solution mayhave poor objective function values in some (non-desired) scenarios (theso-named black swan ones). Those values in the RN  approach can be balanced with the ones insome attractive scenarios. So, the drawback of the approach is the negative impact of the RN solution inthe black swan scenarios occurrence. However, those RN solutions can beprevented by risk averse measures (RAMs), among them, the Stochastic Dominance(SD) functional-based ones. In this talk, two SD-based time-consistent andtime-inconsistent RAMs are considered for two-stage and multistage stochasticproblems. They are based on a set of profiles, each one is included by athreshold to achieve in the objective function and any other function, an upperbound on the threshold achievement shortfall in each scenario, an upper boundon the expected shortfall in the set of scenarios, and  an upper bound on the fraction of scenarioswith shortfall.