Portfolio choice through diversification and stochastic dominance criteria with regulatory and sustainability requirements.

This work aims to address several current challenges in academia and financial industry, and to contribute to the literature by providing advanced methods and models for real-world applications in portfolio management. The first part of the work is devoted to portfolio optimization problems under regulatory and sustainability requirements. To these aims, we develop portfolio selection models that extend the classical Markowitz Mean-Variance approach by a third objective: (i) controlling downside portfolio movements, measured by its Value-at-Risk, and (ii) maximizing the portfolio sustainability, expressed by Environmental, Social, and Governance (ESG) metrics. The latter is obtained by considering two different sustainability indicators, relying on the portfolio expected ESG and on a more robust measure based on the k−sum operator. This novel portfolio ESG indicator considers multiple rating agencies simultaneously and can be interpreted as the investor’s level of sensitivity to the worst ratings from different data providers. In the final part we perform portfolio selection using stochastic dominance and diversification criteria. More precisely, we compare two models based on second-order stochastic dominance conditions, where the portfolio is chosen w.r.t. an “improved” benchmark index. Specifically, given a real-world market index, its “improved” version is obtained by reshaping its variance and skewness appropriately. Finally, we present a general bi-objective model where the aim is to simultaneously maximize a portfolio diversification measure and its expected return. All models are tested with extensive empirical analyses based on real data.