Diffusion processes and their sample paths

An engine, not a camera

This article and the companion paper aim at reviewing recent empirical and theoretical developments usually grouped under the term Econophysics. Since the name was coined in 1995 by merging the words ‘Economics’ and ‘Physics’, this new interdisciplinary field has grown in various directions: theoretical macroeconomics (wealth distribution), microstructure of financial markets (order book modeling), econometrics of financial bubbles and crashes, etc. We discuss the interactions between Physics, Mathematics, Economics and Finance that led to the emergence of Econophysics. We then present empirical studies revealing the statistical properties of financial time series. We begin the presentation with the widely acknowledged ‘stylized facts’, which describe the returns of financial assets—fat tails, volatility clustering, autocorrelation, etc.—and recall that some of these properties are directly linked to the way ‘time’ is taken into account. We continue with the statistical properties observed on order books ...

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Econophysics review: I. Empirical facts

This paper describes and analyses the history of the fundamental equation of modern financial economics: the Black-Scholes (or Black-Scholes-Merton) option pricing equation. In that history, several themes of potentially general importance are revealed. First, the key mathematical work was not rule-following but bricolage, creative tinkering. Second, it was, however, bricolage guided by the goal of finding a solution to the problem of option pricing analogous to existing exemplary solutions, notably the Capital Asset Pricing Model, which had successfully been applied to stock prices. Third, the central strands of work on option pricing, although all recognizably ‘orthodox’ economics, were not unitary. There was significant theoretical disagreement amongst the pioneers of option pricing theory; this disagreement, paradoxically, turns out to be a strength of the theory. Fourth, option pricing theory has been performative. Rather than simply describing a preexisting empirical state of affairs, it altered the...

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An Equation and its Worlds: Bricolage, Exemplars, Disunity and Performativity in Financial Economics

Revue de Metaphysique et de Morale.

Written on the occasion of the centenary of Louis Bachelier's 1900 PhD thesis “Theorie de la speculation”, this paper puts Bachelier into a historical perspective. It explains his role as a pioneer in both mathematical finance and probability theory, and it also gives a careful account of Bachelier's difficult personal and scientific career. This includes a discussion of Poincare's report on the PhD thesis (the report itself with an English translation is reproduced in the appendix), and an explanation for the controversy between Bachelier's work and Paul L´evy's reports on it. The paper also contains a curriculum vitae and a list of the publications of Bachelier is made available.

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Louis Bachelier on the Centenary of Théorie de la Spéculation

We construct a simple trading process that is based on the maximization, at each stage, of the total distributable surplus. We show that this process converges to a Pareto optimal allocation.

Allais' trading process and the dynamic evolution of a market economy

We consider the standard discrete-time model of a frictionless financial market and show that the law of one price holds if and only if there exists a martingale density process with strictly positive initial value. In contrast to the classical no-arbitrage criteria, this density process may change its sign. We also give an application to the CAPM.

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On the law of one price

This paper presents an application of new measures of research excellence, namely Hirsch's index (2005) and derived indexes. It gives a ranking of French departments of Economics, departments of Management and Business schools based on the quality of the academic environment offered by these institutions using these measures. It argues that, since the bulk of the research is done by a very small number of researchers, a greater concentration of the best researchers seems necessary for France to achieve international visibility in Economics and Management.

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Research in economics and management in France: A bibliometric study using the h-index

The h-index is an index recently proposed by Hirsch (2005) to measure scientific achievement by individual scholars. It is a compound measure of publications and citations. We show the robustness of this index. This means that h-index increases with both the number of publications and the number of citations only when these numbers are significant.

https://halshs.archives-ouvertes.fr/halshs-00446309/document

Jean-Michel Courtault

Papers

Louis Bachelier on the Centenary of Théorie de la Spéculation

Allais' trading process and the dynamic evolution of a market economy

On the law of one price

Research in economics and management in France: A bibliometric study using the h-index

On the Robustness of the h-index: a mathematical approach