Portfolio selection is a decision problem that can be formulated as a mathematical optimisation
program. Ever since portfolio selection has been first modelled as a mathematical optimisation
problem, a number of frameworks have emerged. These different frameworks aim to address
the shortfalls and limitations of previous models. However, most of these models rely on the
weak assumption, that the input parameters are known exactly. In the existence of uncertainty
surrounding the input parameters, the outcome of a deterministic optimisation problem might
be overoptimistic with unexpected consequences in certain scenarios. Robust optimisation
deals with the uncertainty surrounding the input parameters. This framework approaches
the uncertainty as deterministic and the solution provides certain guarantees, given that the
realized scenario is within the considered uncertainty set. The consideration of all possible
scenarios leads to more sensible decisions. Robust optimisation frameworks are quite popular
in engineering, whereas an overoptimistic solution might yield a catastrophic outcome. This
thesis aims to investigate the portfolio construction using robust optimisation frameworks. More
specifically, we formulate existing deterministic optimisation models as robust optimisation
models and show that they remain tractable under several types of uncertainty. In particular,
we examine the distributionally robust Omega Ratio maximization (through solving the Omega
Ratio as a convex optimisation problem) and we show that it remains tractable under mixture
distribution, ellipsoidal and box uncertainty. In order to illustrate this, we first show that the
Omega Ratio maximization is a convex optimisation problem. In addition, we show that the
robust counterpart of the Equally-weighted Risk Contribution problem can also be formulated
as a convex optimisation problem. We finally provide numerical evidence that suggest the
existence of a positive premium for the portfolios constructed using robust formulations versus the deterministic models. The numerical evidence is based on real-life data that span the pre-and
post- credit crisis periods.