Multi-intervals robust mean-conditional value-at-risk portfolio optimisation with conditional scenario reduction technique

In this paper, we study mean-conditional value at risk (mean-CVaR) portfolio optimisation with cardinality constraints and short selling under uncertainty. To reduce the level of conservatism, instead of single uncertainty interval, multi-intervals uncertainty sets are considered that are obtained by an efficient scenario reduction technique. It is proven that the proposed robust mean-CVaR model with cardinality constraints and short selling is equivalent to a mixed integer linear programming problem. Finally, using historical data on the S&P index for 2018, we evaluate the efficiency of the proposed models using CVX software in MATLAB. The results show that robust model has relatively low conservatism under multi-intervals uncertainties.