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

Feasibility Conditions of Robust Portfolio Solutions under Single and Combined Uncertainties