L’introduction de la loi de Pareto dans la modélisation financière

Christian Walter (christian.walter@live.fr)

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Abstract: Pareto's distribution became part of financial modelling at the beginning of the 1960s due to the identification of two unidentified properties of this distribution: it is a scale invariant distribution and a limit distribution in probability. These two properties of Pareto's distribution were first introduced by Benoît Mandelbrot, who based Pareto's distribution on Paul Lévy's alpha-stable distributions in the modelling of cotton prices and then of financial assets. This incorporation of the ancient Pareto law into the modelling of the dynamics of the stock market changes its status and confers on it a new life in financial economics, by feeding power laws into the models of the stock market. After having recalled the mathematical properties of the Paretian framework, in particular the paradox of the expected value in a power law, we introduce the modelling debate between a mixture of models (Gaussian for average values and Paretian for extreme values) and a single model for all values (alpha-stable), by the introduction of the extreme value theory and the generalized Pareto distribution. Then we describe the arrival of Pareto's distribution in finance by using Mandelbrot's methodology, which enables us to present the concept of Paretian chance. Finally, we suggest considering the financial practices of private equity as "natural Paretian mathematics", a hypothesis that opens perspectives on the enlargement of rationality to Paretian environments.

Keywords: Power Law; Extreme Values; Paretian Chance; Mandelbrot; alpha-stable Distributions; Lévy Processes; Private Equity; Rationality; valeurs extrêmes; hasard parétien; lois alpha-stables; processus de Lévy; capital-investissement; rationalité; loi de puissance valeurs extrêmes hasard parétien Mandelbrot lois alpha-stables processus de Lévy capital investissement rationalité power law extreme values Paretian chance Mandelbrot alpha-stable distributions Lévy processes private equity rationality; loi de puissance; capital investissement; rationalité power law; extreme values; Paretian chance; alpha-stable distributions; Lévy processes; private equity; rationality (search for similar items in EconPapers)
Date: 2023
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04494659v1
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Published in L'Année Sociologique, 2023, Vilfredo Pareto (1848-1923), 73 (1), pp.113-150. ⟨10.3917/anso.231.0113⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-04494659

DOI: 10.3917/anso.231.0113

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