Robust optimization for enhanced index tracking problem

This thesis addresses the problem of Enhanced Index Tracking (EITP), which consists in constructing portfolios capable of achieving returns superior to a market index while keeping the additional risk within acceptable limits. Two robust approaches are presented: the first relies on robust optimization applied to the Fama-French three- and five-factor models, introducing uncertainty sets on expected returns and on the factor loading matrix; the second employs a Gaussian mixture distribution within the Lower Partial Moments (LPM) framework, where uncertainty on the mixture proportions is handled through 𝜙-divergences. Finally, by means of Lagrange duality, the latter model is shown to be tractable.