Before revision:  In this paper we propose a problem-driven scenario generation methodology for portfolio selection problems using a tail risk measure where the the asset returns have elliptical or near-elliptical distribution. Our approach in effect prioritizes the construction of scenarios in the areas of the distributionwhich correspond to the tail losses of feasible portfolios. The methodology is shown to work particularly well when the distribution of assets returns are positively correlated and heavy-tailed, and the performance is shown to improve as we tighten the constraints on feasible assets .
After revision:  In this paper we propose a problem-driven scenario generation methodology for portfolio selection problems using a tail risk measure , such as conditional value-at-risk. Since tail risk measures only depend on the upper tail of a distribution, standard methods of scenario generation, which typically spread there scenarios evenly across the support of the solution, struggle to adequately represent tail risk well .