M Salahi - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
F Piri - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
F Mehrdoust - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

In the portfolio optimization, the goal is to distribute the fixed capital ona set of investment opportunities to maximize return while managing risk. Risk and return are quantities that are used as input paramete rs for the optimal allocation of the capital in the suggested models.But these quantities are not known at the time of the formulation and solving problem. Thus they should be estimated to solve the problem which might lead to large error. One of the widely usedapproaches to deal with such a situation, is robust optimization. In this paper we study the mean-Conditional Value at Risk (M-CVaR) portfolio selection problems under the estimation risk in meanreturn for both interval and ellipsoidal uncertainty sets. Equivalent formulations of the robustcounterparts are given. At end an example is given to demonstrate the impact of uncertainty.

Portfolio Optimization, Robust Optimization, Value at Risk, Conditional Value at Risk, Conic Optimization