Robust asset allocation problems: a new class of risk measure based models

Many optimization problems involve parameters which are not known in advance, but can only be forecast or estimated. This is true, for example, in portfolio asset allocation. Such problems fit perfectly into the framework of Robust Optimization that, given optimization problems with uncertain parameters, looks for solutions that will achieve good objective function values for the realization of these parameters in given uncertainty sets. Aim of this dissertation is to compare alternative forms of robustness in the context of portfolio asset allocation. Starting with the concept of convex risk measures, a new family of models, called "norm-portfolio" models, is firstly proposed where not only the values of the uncertainty parameters, but also their degree of feasibility are specified. This relaxed form of robustness is obtained by exploiting the link between convex risk measures and classical robustness. Then, we test some norm-portfolio models, as well as various robust strategies from the literature, with real market data on three different data sets. The objective of the computational study is to compare alternative forms of relaxed robustness - the relaxed robustness characterizing the "norm-portfolio" models, the so-called soft robustness and the CVaR robustness. In addition, the models above are compared to a more classical robust model from the literature, in order to experiment similarities and dissimilarities between robust models based on convex risk measures and more traditional robust approaches.