Applications of Set Optimization to Finance

Abstract: Set optimization is a generalization of vector optimization which can be formulated in a complete lattice. In financial risk measurement, set optimization problems arise when capital requirements can be made in a basket of currencies or assets. In this presentations, we will cover the definition of multivariate risk measures as well as primal and dual representations. Additionally, we will discuss, in a dynamic framework, the relation of multivariate risk measures through time and an algorithm for computing these risk measures. Further applications to systemic risk measurement will also be given.