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The building blocks of complexity : a unified criterion and selected applications in economics and finance 1

The analysis of many complex problems and complex dynamic systems shows that there are dependencies between high complexity and the existence of large grids in the underlying structures containing inhomogeneous elements and including an irregular flow of information. This complexity criterion is formulated in a precise way and analysed in different areas of application, particularly for selected problems from economics and finance. We discuss how our criterion can be applied to make complex problems more tractable by exploring structural parameters to control the complexity of problems and systems in complexity engineering. In some areas the criterion is provable in a strong mathematical sense, whereas in others it is confirmed by numerous examples, without finding a counterexample. The areas of application cover: complexity theory, design of efficient algorithms, dynamic systems, chaos theory, neural networks, auctions, capital markets, portfolio credit risk and operational risk management.