On the global minimization of the value-at-risk

In this paper we consider the nonconvex minimization problem of the value at risk VaR that arises from nancial risk analysis By considering this problem as a special linear program with linear complementarity constraints a bilevel linear program to be more precise we develop upper and lower bounds for the minimumVaR and show how the combined bounding procedures can be used to compute the latter value to global optimality A numerical example is provided to illustrate the methodology Dedication With great pleasure we dedicate this paper to a respected pioneer of our eld Professor Olvi L Mangasarian on the occasion of his th birthday The two topics of this paper LPECs and smoothing methods are examples of the vast contributions that Olvi has made in optimization which have bene ted us in many ways and which will continue to bene t us in the future Happy th birthday Olv