The Pareto distribution entered financial modeling at the beginning of the 1960s when two of its properties were identified: that it is a scale invariant distribution and a limit distribution in probability. This incorporation into the modeling of stock market dynamics gives it a new life in financial economics, by injecting power laws into pricing models. After revisiting the mathematical properties of the Paretian framework, we will present the debate on modeling between a mixture of models (Gaussian for average values and Paretian for extreme values) and a single model for all values (alpha-stable), then the arrival of the Pareto distribution in finance by using Mandelbrot’s methodology, which enables us to present the concept of Paretian chance. Finally, we will consider the financial practices of private equity as “natural Paretian mathematics”, a hypothesis that opens perspectives on the extension of rationality to Paretian environments