With Black, Scholes and Merton, modern finance had found one of its most powerful formulations. The price of an option could be deduced from arbitrage reasoning, a dynamic hedging strategy and a differential equation derived from Brownian diffusion. Financial randomness thus became an object that could be calculated, neutralised and almost domesticated. Where Bachelier had introduced the random movement of prices, where Wiener had given a rigorous structure to Brownian motion, where Markowitz had organised portfolio selection under uncertainty, Black, Scholes and Merton took a further step: they showed that a contingent right could be valued on the risk itself. But this construction was based on a particular representation of chance. Price changes are continuous, returns are assumed to be sufficiently close to a normal distribution, and volatility is considered constant or, at the very least, controllable within the framework of the model. The world thus described is unstable, but with a regular instability; uncertain, but with a disciplined uncertainty; random, but with a randomness that is sufficiently smooth to be integrated into an equation. It is precisely this representation that Benoît Mandelbrot disrupts. His contribution to finance does not consist in proposing a new valuation formula comparable to that of Black-Scholes. It is more profound and, in a way, more unsettling. Mandelbrot asserts that financial markets are not only uncertain: they are rough. They do not always fluctuate according to a smooth and continuous geometry; they experience breaks, accelerations, discontinuities, concentrations of volatility, and extreme events more frequently than the Gaussian model predicts. With him, finance can no longer be content with thinking of risk as a regular dispersion around an average. It must learn to think about irregularity itself. Benoît Mandelbrot was born in Warsaw on 20 November 1924 into a Jewish family of Lithuanian origin. His father was a businessman and his mother a doctor. The Mandelbrot family belonged to that world of Central Europe where scientific culture, languages, migration and historical uncertainty were closely intertwined. Very early on, the young Benoît was shaped by a demanding intellectual environment. His uncle, Szolem Mandelbrojt[1], was a renowned mathematician, a professor at the Collège de France, a specialist in analysis and close to the Bourbaki group[2]. This family presence played an important role in his intellectual orientation, even though Mandelbrot would always remain at a distance from established schools and mathematical orthodoxies. In 1936, faced with the growing dangers in Eastern Europe, the family left Poland for France. Benoît Mandelbrot arrived in Paris at the age of eleven. This geographical and cultural break was decisive. It exposed him both to the richness of the French intellectual system and to the violence of history. During the Second World War, the family had to take refuge in the provinces to escape persecution. These war years interrupted normal schooling, but they developed a very particular form of visual and intuitive intelligence in Mandelbrot. He would later say that he often learned better through images, shapes and geometric analogies than through traditional linear demonstrations. This uniqueness made him stand out very early on. After the war, he entered the École Polytechnique, where he benefited in particular from the teaching of Gaston Julia[3], one of the great names in the theory of complex functions. From the beginning of the 20th century, Julia had studied mathematical objects that would later become central to fractal theory. At the time, these shapes were still largely considered as analytical curiosities, or even as mathematical monsters: sets that were difficult to visualise, irregular, and beyond the reach of classical geometric intuition. Mandelbrot would later find in them one of the profound sources of his work. After the École Polytechnique, he continued his studies in the United States, notably at the California Institute of Technology, then returned to France before working at the CNRS. But he did not fully identify with the dominant style of post-war French mathematics. The Bourbaki group, to which his uncle was close, promoted very abstract, axiomatic, structural mathematics, detached from immediate applications. Mandelbrot, on the contrary, was attracted to concrete phenomena, irregular shapes, empirical data, and misclassified objects. He was interested in linguistics as much as in turbulence, the geography of coastlines, the distribution of income, transmission noise in telephone lines or variations in financial prices. He does not seek only to demonstrate; he seeks to see. This intellectual freedom explains his departure for the United States. In 1958, he joined the IBM laboratories, where he remained for several decades. This choice was fundamental. IBM offered him a rare environment: the opportunity to work at the frontier of mathematics, computer science, physics and economics, without being confined by the constraints of a traditional university department. Above all, IBM gave him access to powerful computers, which would play a decisive role in the visualisation of fractal objects. For Mandelbrot, the computer was not just a calculating machine; it became an instrument for geometric exploration. It made it possible to make visible shapes that classical mathematics had foreseen but could not yet fully represent. The word “fractal” would not appear until later, in the 1970s. Mandelbrot coined it from the Latin fractus, which means broken, fragmented, irregular. A fractal is a shape whose complexity is repeated at different scales. A coastline, a cloud, a mountain, a vascular network or a fern all have this property: when you zoom in on a part, you find patterns that resemble the overall structure. This is self-similarity or scale invariance. These shapes cannot be described correctly by classical Euclidean geometry. A line, a circle, a triangle or a sphere are suitable for representing an ideal, smooth and regular world; but the real world is often rough, fragmented and uneven. Mandelbrot’s great insight was to show that this roughness is not pure disorder. It has a structure. It can be measured, described, compared. The apparent chaos conceals a form of order, but an order that is different from that of classical geometry. Where Euclid describes simple shapes, Mandelbrot seeks to describe

Founding member of CIRET Professor René Passet, a founding member of the Centre International de Recherches et Études Transdisciplinaires (CIRET), who has just passed away at the age of 99, is the French economist who succeeded in liberating economic discourse from its confinement in order to consider it within the infinitely broader context of life on Earth.  Contemporary economic discourse has its origins in the image of the pin factory put forward by Adam Smith in his seminal work The Wealth of Nations. We are familiar with the principle. A craftsman, working alone in his workshop, can at best produce 10 pins in a day’s work. Therefore, ten craftsmen will produce around one hundred. However, ten workers working together in a machine-equipped factory and dividing the work between them may produce 10,000 pins, i.e., 1,000 each. This represents a 10,000% increase in productivity. National prosperity will therefore increase by the same amount. To this is added the principle of comparative advantage, which suggests that the English should manufacture and sell textiles to the Portuguese, in return for which the Portuguese will sell them Port wine. The entire contemporary economic system is based on this dual principle.  The problem is that it oversimplifies reality. First question: Is a factory worker, who spends their time performing repetitive tasks that are imposed on them, more or less happy than a craftsman in their small workshop? Economists are more or less silent on this point. Second question: Is the desired abundance compatible with the quantity of raw materials and energy available in the Earth’s subsoil, and can the waste from industrial activity be absorbed by the Earth without causing damage? The classical economist is also silent on this point. And so it is René Passet who, in his best-known book, L’Economique et le Vivant, asks whether the principle of economic efficiency is indeed compatible with the principle of preserving and reproducing living organisms. However, this question has become fundamental to the very survival of humanity. Some people suggest that the ‘green economy’, ‘sustainable development’ and ‘renewable energies’ will make it possible to ensure compatibility between economic life and the preservation of living organisms. However, these are merely words. As Nicholas Georgescu-Roegen, who was an economist but also a physicist, clearly demonstrated, ‘economic development’ manifests itself as a local expression of negentropy. And energy consumption, in whatever form, cannot sustainably exceed the amount of energy available. And as soon as energy consumption on Earth exceeds the supply of solar energy, we have to draw on reserves, which are limited. We can see this clearly, for example, in the case of ‘rare earth elements’, which are now indispensable for electronics.  The question, in line with the logic of the living world as espoused by René Passet, is how we got to this point. This is the subject of the comprehensive work he published under the title Les grandes représentations du monde et de l’économie à travers l’histoire (‘The Major Representations of the World and the Economy Throughout History’), which spans over 900 large-format pages. We will not attempt here to present a summary of this work, which would inevitably be incomplete. What we will take away from it is that the economic discourse, as it currently drives the majority of humanity, is an ideological construct. This ideological construct draws on philosophical currents that can be traced through history, and which have led to a worldview characteristic of the ‘modern world’. This worldview is leading humanity towards catastrophe, and that is why the assertion of a critical mindset is not only necessary but urgent, given the increasing effects of global warming and the poisoning of the biosphere.  I will conclude with a personal reflection. In 1975, René Passet was the chair of my doctoral thesis examination board at what was then the University of Paris 1. I cannot imagine any professor of economics other than him who would have accepted a topic that fell more within the domain of anthropology than economics, and whose opening words were borrowed from Prof. Jacob Viner, ‘Economics is what economists say’. The passing of a man who will probably be recognised in the future as a pioneer therefore places a duty on us at CIRET to continue along the path he has thus charted.  Hubert Landier René Passet, L’économique et le vivant, Petite bibliothèque Payot, 1983. René Passet, Les grandes représentations du monde et de l’économie à travers l’histoire, Les Liens qui Libèrent, 2010.

By Jean-Jacques Pluchart On Tuesday, 14 April 2026, a tribute will be paid to the memory of the economist Roger Guesnery, Honorary President of PSE-Paris School of Economics and Professor Emeritus at the Collège de France, holding the Chair in ‘Economic Theory and Social Organisation’. His work contributed to advances in research on the functioning of public services: asymmetric information between the State and citizens, international coordination in the fight against global warming, rational expectations of agents, and the ‘second-best’ equilibrium, among other topics. Roger Guesnery co-founded DELTA (Département et laboratoire d’économie théorique et appliquée – Department and Laboratory of Theoretical and Applied Economics) with François Bourguignon. At the request of François Furet, then President of the EHESS, he was also the first head of the doctoral programme ‘Economic Analysis and Policy’ from 1981 to 1991. He served as Chair of the Board of Governors of the Paris School of Economics, and was a member of the Conseil d’analyse économique (Economic Analysis Council) and of the editorial boards of several renowned professional journals. He was Co-Editor-in-Chief of Econometrica (from 1984 to 1989), President of the European Economic Association (1994), President of the Econometric Society (1996) and President of the Association Française de Sciences Économiques (2003). He was awarded the CNRS Silver Medal (1993) and appointed as an Honorary Foreign Member of the American Economic Association (since 1997) and as a member of the American Academy of Arts and Sciences. The event brought together, in the Daniel Cohen Amphitheatre of the Paris School of Economics, around forty economics researchers, including two Nobel Prize winners and several professors from the Collège de France, the EHESS and the world’s leading universities.  The speeches, which were often moving, provided an opportunity to appreciate Roger Guesnery’s human qualities, as well as the vitality of French research in economics – and especially in econometrics – which has already been honoured with five Nobel Prizes. Roger Guesnery’s latest publications Guesnerie R. et Stern R., Deux économistes face aux enjeux climatiques, Paris, Le Pommier, coll. « Essais – Savoirs et débats économiques », 2013, 128 p. Guesnerie R., Pour une politique climatique globale. Blocages et ouvertures, Paris, Éditions Rue d’Ulm, collection du CEPREMAP, 2010. Geoffard P.-Y., Guesnerie R. et Le Grand J., La Santé par quels moyens et à quels prix ?, Paris, PUF, 2010.

By Philippe Alezard With Wiener, modern finance had found a way to give uncertainty a mathematical form. Brownian motion made it possible to conceive of price fluctuations as the cumulative effect of an infinite number of elementary shocks – random, unpredictable, yet nevertheless capable of being placed within a rigorous probabilistic framework. In other words, uncertainty ceased to be a mere market intuition and became a mathematical object. However, this initial breakthrough did not exhaust the issue. For knowing that prices fluctuate according to a stochastic dynamic does not yet tell us how an investor should behave in the face of this instability. Once uncertainty had been described, the next step was to structure how it was used. It is precisely at this point that Harry Markowitz enters the picture. Whereas Wiener provided finance with the probabilistic grammar of uncertainty, Markowitz developed its decision-making logic. His primary concern was no longer the evolution of a price over time, but rather the selection of a portfolio of assets in a world where the future remains irreducibly uncertain. With him, finance crossed a new threshold of formalisation: it no longer contented itself with modelling market movements, but sought to determine how a rational agent should allocate their capital within these movements. The only son of a Chicago grocery store owner couple, Harry Markowitz was born in Chicago on 24 August 1927. At secondary school, his first interests were physics and philosophy [1]. One of the arguments that particularly impressed him was David Hume’s claim that, even if we drop a ball a thousand times and it falls to the ground each time, we have no necessary proof that it will fall the thousand and first time. In 1947, he enrolled at the University of Chicago to study for a Bachelor of Philosophy degree on the OII (‘Observation, Interpretation and Integration’) programme, but by 1950, he was drawn to the economics of uncertainty. At that time, he was interested in the work of von Neumann [2] and Morgenstern on expected utility, as well as that of Milton Friedman and Leonard Savage on the utility function. Having never taken a single finance course and never bought a single share, he was invited to join the renowned Cowles Commission for Research in Economics [3], an institution that has produced twelve Nobel Prize winners in Economics to date, including Markowitz himself. At the time, its director was Tjalling Koopmans [4], who would go on to win the Nobel Prize in 1975 for his work on the theory of the optimal allocation of resources. Among the lecturers who would teach the young Markowitz were, notably, Milton Friedman and Leonard J. Savage [5]. For the record, it is to the latter that we owe the rediscovery of Louis Bachelier’s thesis, which he had Paul Samuelson read. It was also while reading John Burr Williams’ The Theory of Investment Value [6] that Markowitz came up with the idea for his doctoral thesis topic. As he himself recounts in his autobiography, published on the occasion of his Nobel Prize award, ‘Williams proposed that the value of a share should be equal to the present value of its future dividends. Since future dividends are uncertain, I interpreted Williams’ proposition as meaning that a share should be valued on the basis of its expected future dividends. But if the investor were concerned only with the expected values of securities, he or she would be concerned only with the expected value of the portfolio; and, to maximise the expected value of a portfolio, it would be sufficient to invest in a single security. I knew that this was neither how investors behaved nor how they should behave. Investors diversify because they are as concerned about risk as they are about return.” Markowitz’s insight [7], though seemingly simple, is in fact of considerable significance. Prior to him, financial analysis tended to assess investments primarily on an individual basis, based on their promised returns, their soundness or their reputation. Markowitz radically shifted the focus of the problem by demonstrating that, from the investor’s perspective, the relevant unit is not the individual asset, but the portfolio as a whole. In his seminal article, ‘Portfolio Selection’, published in the March 1952 issue of the Journal of Finance, he proposed representing a portfolio not as the simple sum of several securities, but as an overall structure resulting from their combination. This is because what matters is not only the intrinsic quality of each asset, but the combination of their behaviours, since the risk of a portfolio depends not only on the risk inherent in each security, but also on how these securities vary in relation to one another. The financial decision thus ceases to be a simple matter of selecting good securities and becomes a question of portfolio composition. This shift is decisive, as it reveals that risk itself cannot be considered in a purely individual manner. An asset may be highly volatile when considered in isolation, but it can become fully acceptable within a portfolio if, through its relationships with other assets, it helps to stabilise the whole. Conversely, apparently safe securities, if they all react in the same way to the same events, can collectively generate greater fragility than one might imagine. In this way, Markowitz introduces the idea that financial rationality is not a property of individual instruments, but of the way they are combined. This idea is formulated through the distinction between expected return and risk. According to Markowitz, the investor optimises this return–risk pair at the portfolio level, either by seeking the highest return for a given risk or by seeking the lowest risk for a given return. It thus becomes possible to represent the portfolio using utility functions that depend solely on the expected return, i.e., the mathematical expectation, and on a measure of risk, i.e., variance. In Markowitz’s work, variance derives its legitimacy not from its common use in statistics, but from its economic relevance. It is justified by the