Christian Walter

While in medicine, comparison of the data supplied by a clinical syndrome with the data supplied by the biological system is used to arrive at the most accurate diagnosis, the same cannot be said of financial economics: the accumulation of statistical results that contradict the Brownian hypothesis used in risk modelling, combined with serious empirical problems in the practical implementation of the Black-Scholes-Merton model, the benchmark theory of mathematical finance founded on the Brownian hypothesis, has failed to change the Brownian representation, which has endured for more than fifty years despite the extent of its invalidation by experience. Without any statistical foundations, one mathematical representation has become the established approach, acting in the minds of practitioners as a “prenotion” in the sense the word is used by Durkheim, i.e. a “schematic, summary representation” which has produced a kind of spontaneous epistemology. The question arises of the persistence of this mathematical representation, which has been the basis for every financial risk modelling approach: how can its long life be explained? How was this spontaneous epistemology formed, and why did it prove to be so persistent? To address this question and offer an answer, I will test the various dynamics of scientific knowledge used with reference to financial modelling. All these dynamics are specific ways of describing the relationship between knowledge of a phenomenon and the phenomenon itself. Observing that it is impossible for the positivist approach to solve the financial puzzle, I turn to the three principal postpositivist dynamics, developed by Kuhn, Lakatos and Quine. I shall try to make to speak these representations of science for financial research, in order to reflect on the dominance of the Brownian representation in finance. We shall see that none of the epistemologies examined can explain why the Brownian representation continues to be used in mathematical finance research. I shall then propose an alternative hypothesis, concerning a significant pervading mental model that has irrigated both academics and practitioners in the financial sector: the “principle of continuity” introduced into economics by Marshall in. I consider that this principle of continuity has become a “persistent idea” in the form of a viral approach to representations, and I give this persistent idea the metaphorical name of the “Brownian virus”. Then, to explain the spread of this Brownian virus through the financial sector, the contamination of financial practices by this mental representation founded on the principle of continuity, I introduce the concept of the “financial Logos”, a discourse that structures practices and organisations, calculations, prudential regulations and accounting standards, leading to a general financialisation of society from the 1980s onwards.

The protection of human rights has become one of the main characteristics of international law of the post-World War II era and with the breakdown of the Soviet empire democracy itself is gradually moving into the focus of international legal analysis. Hence, it is necessary to conceive the concept of militant democracy also from an international legal perspective, which raises several fundamental questions: Do international human rights pose constraints on national constitutional norms designed to defend democracy, and if so, how do these limits look like? And conversely: can human rights be used as an argument in favor of militant democracy? Are there other international legal norms designed to preserve democracy? The Chapter, first, analyzes the impact that international human rights standards on the concept of militant democracy. In a second step, other forms of internationalized militant democracy, notably the mechanisms established by Article 7 of Treaty on European Union and Article 8 of the Statute of the Council of Europe, are being looked into. The analysis leads to the conclusion that militant democracy is currently being internationalized as a legal and political concept.

La modélisation financière moderne instrumente massivement des lois d'échelle pour la formalisation des fluctuations des marchés, à travers l'usage des processus aléatoires dans les équations de comportement des cours boursiers. D'abord implicites, présentes dans le mouvement brownien mais non perçues en tant que telles, les lois d'échelle sont réapparues explicitement comme enjeu de la modélisation depuis que les autorités de tutelle des marchés financiers ont attiré l'attention des établissements bancaires sur le problème du contrôle des risques, mal quantifiés par les distributions gaussiennes classiques. On présente les éléments de ce débat, en adoptant comme fil conducteur la postérité des modèles fractals de Mandelbrot dans le sillage desquels s'inscrivent les principaux conflits de modélisation des variations boursières depuis les quarante dernières années. On montre que la question de l'existence de lois d'échelle renvoie à la question plus fondamentale de la nature du temps des marchés.

In this chapter, one considers finance at its very foundations, namely, at the place where assumptions are being made about the ways to measure the two key ingredients of finance: risk and return. It is well known that returns for a large class of assets display a number of stylized facts that cannot be squared with the traditional views of 1960s financial economics (normality and continuity assumptions, i.e. Brownian representation of market dynamics). Despite the empirical counterevidence, normality and continuity assumptions were part and parcel of financial theory and practice, embedded in all financial practices and beliefs. Our aim is to build on this puzzle for extracting some clues revealing the use of one research strategy in academic community, model tinkering defined as a particular research habit. We choose to focus on one specific moment of the scientific controversies in academic finance: the ‘leptokurtic crisis’ opened by Mandelbrot in 1962. The profoundness of the crisis came from the angle of the Mandelbrot’s attack: not only he emphasized an empirical inadequacy of the Brownian representation, but also he argued for an inadequate grounding of this representation. We give some insights in this crisis and display the model tinkering strategies of the financial academic community in the 1970s and the 1980s.