8.1 Introduction

The purpose of this chapter is to examine the usefulness of ideas of robust optimization. We shall look at potential applications in the area of financial forecasting. In keeping with the general theme of this book, we shall focus on expected returns forecasting, and how forecasting and robust optimization can be entered into jointly in a beneficial way. In the process of carrying out these tasks, we shall overview much of the current research in robust optimization; not least because it is an area of great commercial interest.

Robust optimization can have wide applications in finance, including in portfolio construction, option pricing and hedging, and risk management. Robust optimization deals with uncertainty. The robust optimization literature tries to address directly both parameter uncertainly (arising because of the imperfect data available to practitioners and researchers), and also model uncertainty (or the possibility of incorrect structure in the underlying model used). The purpose is to come up with more stable, relevant portfolios that are less prone to data and other errors. We will examine these concepts in more detail.

Note that there is an important distinction in this literature between risk and uncertainty. In simple terms, risk is when you can capture model variation by assigning priors and probabilities to parameters or structures; uncertainty is when you cannot assign probabilities. The distinction is profound, not least because of the experimental evidence of ambiguity (uncertainty) aversion, which is illustrated by Knight s and Ellsberg s Urns. These are...