The New Role of Mathematical Risk Modeling and Its Importance for Society

Abstract

This book on risk and security is an example for the new role of mathematical modeling in science. In Newtonian times, mathematical models were mainly applied to physics and astronomy (e.g., planetary systems) as definitive mappings of reality. They aimed at explanations of past events and predictions of future events. Models and theories were empirically corroborated or falsified by observations, measurements and lab experiments. Mathematical predictions were reduced to uniquely determined solutions of equations and the strong belief in one model as mapping of reality. In probabilistic models, extreme events were underestimated as improbable risks according to normal distribution. The adjective “normal” indicates the problematic assumption that the Gaussian curve indicates a kind of “natural” distribution of risks ignoring the fat tails of extreme events. The remaining risks are trivialized. The last financial crisis as well as the nuclear disaster in Japan are examples of extreme events which need new approaches of modeling.