Worst-case CVaR based portfolio optimization models with applications to scenario planning

This article studies three robust portfolio optimization models under partially known distributions. The proposed models are composed of min-max optimization problems under the worst-case conditional value-at-risk consideration. By using the duality theory, the models are reduced to simple mathematical programming problems where the underlying random variables have a mixture distribution or a box discrete distribution. They become linear programming problems when the loss function is linear. The solutions between the original problems and the reduced ones are proved to be identical. Furthermore, for the mixture distribution, it is shown that the three profit-risk optimization models have the same efficient frontier. The reformulated linear program shows the usability of the method. As an illustration, the robust models are applied to allocations of generation assets in power markets. Numerical simulations confirm the theoretical analysis.