Robust portfolio optimisation with filtering uncertainty

This thesis focuses on how portfolio optimisation can be carried out under different types of uncertainty, which we often measure through the use of filters. Chapter 1 motivates the problem, gives an overview of the thesis and covers some necessary background material. Chapter 2 deals with uncertainty in the covariance matrix and how by identifying different regimes we can solve optimisation problems of interest to practitioners. Chapter 3 focuses on the uncertainty over tail events and how we can not only extract relevant information by filtering the data but also how we can use that information to construct a portfolio optimisation problem that acts on it. In Chapter 4 we address the lack of tractability for general relative robust portfolio optimisation problems and how one can overcome this so as to make it a viable tool. Chapter 5 considers the problem of uncertainty in the filter itself and how this uncertainty can be fully incorporated in the portfolio optimisation problem. Finally in Chapter 6 we conclude and propose topics for future research.