Laureano Escudero (Universidad Rey Juan Carlos): On the Stochastic Dominance functional-basedrisk averse versions in mathematical optimization under uncertainty

Información (pendiente de confirmación)

Very 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.