Robust portfolio optimization

The Markowitz mean-variance portfolio optimization is a well known and also widely used investment theory in allocating the assets. However, this theory is also familiar with the extremely sensitive outcome by the small changes in the data. Ben-Tal and Nemirovski [3] therefore introduced the robust counterpart approach of the optimization problem to provide more conservative results. And on the ground of their work, Schottle [26] furthermore proposed the local robust counterpart approach with the smaller uncertainty set. This paper presents an overview of the local robust counterpart approach of the optimization problem with uncertainty. The classical mean-variance portfolio optimization problem is presented in the first place, and followed by the description of the general convex conic optimization problem with data uncertainty. Afterwards, the concept of the local robust counterpart approach of the optimization problem will be discussed and then applied into the foreign currency market