Derivatives and subderivatives of buffered probability of exceedance

Abstract In this letter, we study the derivatives and subderivatives of buffered probability of exceedance (bPOE), in which we provide the mathematical expressions with rigorous proofs for the case when bPOE is smooth. Furthermore, we extend the study to a general non-smooth case for which a set of quasigradients are explored, under a mild assumption, i.e., the corresponding random function with respect to the decision variable is convex.