Primal and dual robust counterparts of uncertain linear programs: an application to portfolio selection.

This paper proposes a family of robust counterpart for uncertain linear programs (LP) which is obtained for a general definition of the uncertainty region. The relationship between uncertainty sets using norm bodies and their corresponding robust counterparts defined by dual norms is presented. Those properties lead us to characterize primal and dual robust counterparts. The researchers show that when the uncertainty region is small the corresponding robust counterpart is less conservative than the one for a larger region. Therefore, the model can be adjusted by choosing an appropriate norm body and the radius of the uncertainty region. We show how to apply a robust modeling approach to single and multi-period portfolio selection problems and illustrate the model properties with numerical examples.