Correlation, Risk and Crisis

Alexander N Gorban (University of Leicester, UK) 

with Elena V Smirnova (Siberian Federal University, Russia) and Tatiana Tyukina (University of Leicester, UK)


In many areas of practice, from physiology to economics, psychology, and engineering we have to analyse behavior of groups of many similar systems, which are adapting to the same or similar environment. Groups of humans in hard living conditions (Far North city, polar expedition or a hospital, for example), trees under influence of anthropogenic air pollution, rats under poisoning, banks in financial crisis, enterprises in recession and many other situations of that type provide us with plenty of important problems, problems of diagnostics and prediction. 

For many such situations it was found that the correlations between individual systems are better indicators than the value of attributes. More specifically, in thousands of experiments it was shown that in crisis, typically, even before obvious symptoms of crisis appear, the correlations increase, and, at the same time, variance (volatility) increases too. After the crisis achieves its bottom, it can develop into two directions: recovering (both correlations and variance decrease) or fatal catastrophe (correlations decrease, but variance continue to increase). 


A general approach to explain this effect through the dynamics of adaptation is developed in terms of factor-resource models. We represent systems adapting to stress as the systems which optimise distribution of available resources for neutralisation of different aggressive factors. Different organisation of interaction between factors (Liebig's vs synergistic systems) lead to different adaptation dynamics. This gives an explanation of qualitatively different dynamics of correlation under different types of load.


AN Gorban, EV Smirnova, TA Tyukina. Correlations, Risk and Crisis: from Physiology to Finance. E-print. Available at SSRN

AN Gorban, EV Smirnova, TA Tyukina. General Laws of Adaptation to Environmental Factors: From Ecological Stress to Financial Crisis (28 May 2009). Available at SSRN

Anna Karenina principle explains bodily stress and stockmarket crashes (University of Leicester, Press Office)

Plants and Animals Under Stress May Provide the Key to Better Stock Market Predications.

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