Feasibility conditions of robust portfolio solutions with single and combined uncertainties

In this paper, we derive the feasibility conditions for the robust counterparts of the uncertain Markowitz model. Our study is based on ellipsoidal, box, polyhedral uncertainty sets and also the uncertainty sets obtained from their combinations. We write the uncertain Markowitz problem in a quadratically constrained convex quadratic programming form and the uncertain sets are converted into their quadratic forms for the derivation. The feasibility conditions of robust solutions which we obtained are in the form of positive semi-definite matrices. The study can be useful for deriving the robust counterparts of the combined uncertainties, which in general is difficult to find out.