The building blocks of complexity: a unified criterion and selected applications in risk management

The analysis of many complex problems and complex dynamic systems suggests that there are dependencies between high complexity and properties of the underlying structures, as the existence of large grids, non-regularities and inhomogeneous structures and irregular flows of information. These observations indicate the existence of a unified criterion that defines structural elements of complex entities. We present the idea of such a criterion basing on concepts from computational and parametric complexity theory and analyse its impact in financial risk management. It is shown that selected real-world problems in risk managements are complex in the sense of NP-completeness. Here the criterion is used to analyse the structural reasons for the proved complexity. We show how selected risk management methods fit into the picture of our complexity criterion and derive some implications for the future generation of risk management methods from the viewpoint of complexity.