Complexity, Power Laws and a Humean Argument in Risk Management: The Fundamental Inadequacy of Probability Theory as a Foundation for Modeling Complex Risk in Banking

Abstract

Whenever risk managers are confronted with deep uncertainty and organized complexity, probabilistic inference methods are used. These seem able to allow for crisp inputs and precise results. However, as has been noted by several thinkers (e.g., von Hayek in Studies in philosophy, politics and economics, Routledge, London, 1967; Weaver in American Scientist, 36: 536–544, 1948), such methods cannot be used effectively in such situations. This might basically sound like old wine in a new bottle and, in fact, objections to, and limitations of conventional, i.e., probabilistic risk modeling are anything but unheard of in the literature of banking and finance. However, this paper introduces for the first time an argument, inspired by reflections on the old riddle of induction, from which those shortcomings of the limited suitability of probability can be derived. It demonstrates that any choice of a particular probability distribution for a given risk management purpose is necessarily arbitrary, i.e., it is not grounded in the data but in the choices of the statistician or risk manager, and cannot be justified by appealing to something more objective. Thereby, this paper unmasks the illusion that financial data and extreme losses are well-described by non-standard probability functions such as power laws that have been embraced at the expense of bell curves in the aftermath of the global financial crisis of 2008. Moreover, although we do not propose a positive solution, we believe that articulating the real, and as yet unnoticed, source of the problem is a key step towards developing a principle and tractable response.