Robust portfolio selection with polyhedral ambiguous inputs

Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral ambiguity sets of the scenarios. The models are linear programs in the both cases. Using a portfolio of USA stock market, we apply the buy-and-hold strategy to evaluate the model's performance.
We found that the robust models have almost the same out-of-sample performance, and outperform the nominal model. However, the robust model with correlated polyhedral results in more conservative solutions.