%0 Journal Article %T (Sub-)Differentiability of Probability Functions with Elliptical Distributions %+ Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie (EDF R&D OSIRIS) %+ IFP Energies nouvelles (IFPEN) %A van Ackooij, Wim %A Aleksovska, I. %A Munoz-Zuniga, M. %< avec comité de lecture %@ 1877-0533 %J Set-Valued and Variational Analysis %I Springer %V 26 %N 4 %P 887-910 %8 2018-12 %D 2018 %R 10.1007/s11228-017-0454-3 %K Stochastic optimisation %K Probabilistic constraints %K Chance constraints %K Gradients of probability functions %Z MSC 90C15; MSC 90C30 %Z Mathematics [math]/Probability [math.PR]Journal articles %X In this paper we investigate probability functions acting on nonlinear systems wherein the random vector can follow an elliptically symmetric distribution. We provide first and second order differentiability results as well as readily implementable formulæ. We also demonstrate that these formulæ can be readily employed within standard non-linear programming software through a set of illustrative numerical experiments. %G English %L hal-02013571 %U https://ifp.hal.science/hal-02013571 %~ IFP %~ INSMI %~ EDF