Robust Mean-Conditional Value at Risk Portfolio Optimization

In ‎the ‎portfolio ‎optimization, ‎the ‎goal ‎is ‎to ‎distribute ‎the ‎ fixed capital ‎on a‎ ‎set ‎of‎investment ‎opportunities ‎to ‎maximize ‎return ‎while ‎managing ‎risk. ‎Risk ‎and ‎return ‎are ‎quantiti es ‎that ‎are ‎used ‎as ‎input ‎paramete‎rs ‎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 ‎shou ld ‎be ‎estimated ‎to ‎solve ‎the ‎problem ‎which ‎might ‎lead ‎to ‎large ‎error.‎ One of the widely used approaches to deal with such a situation, is robust optimization. In this paper we study the meanConditional Value at Risk (M-CVaR) portfolio selection problems under the estimation risk in mean return for both interval and ellipsoidal uncertainty sets. Equivalent formulations of the robust counterparts are given. At end an example is given to demonstrate the impact of uncertainty.