Louis Bachelier

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"Bachelier" redirects here. For the artist, see Jean-Jacques Bachelier.
Louis Bachelier
Louis Bachelier, aged 15
Born (1870-03-11)March 11, 1870
Le Havre, France
Died April 28, 1946(1946-04-28) (aged 76)
Saint-Servan-sur-Mer, France
Nationality French
Fields Mathematics
Institutions University of Paris
Université de Franche-Comté (Besançon)
Université de Dijon
Université de Rennes
Alma mater University of Paris
Doctoral advisor Henri Poincaré
Known for Contributions to mathematical finance

Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 – April 28, 1946)[1] was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis The Theory of Speculation, (published 1900).

His thesis, which discussed the use of Brownian motion to evaluate stock options, is historically the first paper to use advanced mathematics in the study of finance. Thus, Bachelier is considered a pioneer in the study of financial mathematics and stochastic processes.

Early years[edit]

Bachelier was born in Le Havre. His father was a wine merchant and amateur scientist, and the vice-consul of Venezuela at Le Havre. His mother was the daughter of an important banker (who was also a writer of poetry books). Both of Louis' parents died just after he completed his high school diploma ("baccalauréat" in French), forcing him to take care of his sister and three-year-old brother and to assume the family business, which effectively put his graduate studies on hold. During this time Bachelier gained a practical acquaintance with the financial markets. His studies were further delayed by military service. Bachelier arrived in Paris in 1892 to study at the Sorbonne, where his grades were less than ideal.

The Thesis[edit]

Bachelier's thesis was not well received because it attempted to apply mathematics to an unfamiliar area for mathematicians.[2] However, his instructor, Henri Poincaré, is recorded to have given some positive feedback (though socially insufficient for finding an immediate teaching position in France at that time). For example, Poincaré called his approach to deriving Gauss' law of errors

The thesis received a grade of honorable, and was accepted for publication in the prestigious Annales Scientifiques de l’École Normale Supérieure. While it did not receive a mark of très honorable, despite its ultimate importance, the grade assigned is still interpreted as an appreciation for his contribution. Jean-Michel Courtault et al. point out in "On the Centenary of Theorie de la Speculation" that honorable was "the highest note which could be awarded for a thesis that was essentially outside mathematics and that had a number of arguments far from being rigorous." The positive feedback from Poincaré can be attributed[by whom?] to his interest in mathematical ideas, not just rigorous proof.

Academic career[edit]

For several years following the successful defense of his thesis, Bachelier further developed the theory of diffusion processes, and was published in prestigious journals. In 1909 he became a "free professor" at the Sorbonne. In 1914, he published a book, Le Jeu, la Chance, et le Hasard (Games, Chance, and Randomness), that sold over six thousand copies. With the support of the Council of the University of Paris, Bachelier was given a permanent professorship at the Sorbonne, but World War I intervened and Bachelier was drafted into the French army as a private. His army service ended on December 31, 1918.[3] In 1919, he found a position as an assistant professor in Besançon, replacing a regular professor on leave.[3] He married Augustine Jeanne Maillot in September 1920 but was soon widowed.[3] When the professor returned in 1922, Bachelier replaced another professor at Dijon.[3] He moved to Rennes in 1925, but was finally awarded a permanent professorship in 1927 at Besançon, where he worked for 10 years until his retirement.[3]

Besides the setback that the war had caused him, Bachelier was blackballed in 1926 when he attempted to receive a permanent position at Dijon. This was due to a "misinterpretation" of one of Bachelier's papers by Professor Paul Lévy, who—to Bachelier's understandable fury—knew nothing of Bachelier's work, nor of the candidate that Lévy recommended above him. Lévy later learned of his error, and reconciled himself with Bachelier.[4]

Although Bachelier's work on random walks was more mathematical and predated Einstein's celebrated study of Brownian motion by five years, Lord Rayleigh's work on a heavy particle in a single temperature buffer gas [5] predates Bachelier's work by nine years and is among the first descriptions of Brownian motion to describe the relation between the dissipation and fluctuations of a stochastic system, also known as the fluctuation-dissipation theorem.


Also published as a book, Bachelier 1900b
Republished in a book of combined works, Bachelier 1995
Translated into English, Cootner 1964, pp. 17–78
Translated into English with additional commentary and background, Bachelier et al. 2006
Translated into English, May 2011
Republished in a book of combined works, Bachelier 1995
Republished, Bachelier 1992
Republished, Bachelier 1993
Erratum, Bachelier 1941b

See also[edit]


  1. ^ Felix 1970, pp. 366–367
  2. ^ Weatherall, James Owen (January 2, 2013). The Physics of Wall Street: A Brief History of Predicting the Unpredictable. Houghton Mifflin Harcourt. p. pp.10-11. ISBN 978-0547317274. 
  3. ^ a b c d e Jean-Michel Courtault; Yuri Kabanov; Bernard Bru; Pierre Crépel; Isabelle Lebon; Arnaud Le Marchand (2000). "Louis Bachelier on the Centenary of Théorie de la Spéculation". Mathematical Finance 10 (3): 339–353. doi:10.1111/1467-9965.00098. 
  4. ^ Mandelbrot, Benoit; Hudson, Richard L. (2014), The Misbehavior of Markets: A Fractal View of Financial Turbulence, Basic Books, pp. 48–49, ISBN 9780465004683 .
  5. ^ Rayleigh, Lord 1891 Phil. Mag. 32, 424
  6. ^ Rietz H. L. (1914). "Revew: Calcul des Probabilités by Louis Bachelier. Tome I". Bull. Amer. Math. Soc. 20 (5): 268–273. doi:10.1090/s0002-9904-1914-02484-x. 


  • Bachelier, L. (1900b), Théorie de la spéculation, Gauthier-Villars 
  • Bachelier, L. (1913b), Les probabilités semi-uniformes, Comptes-rendus des Séances de l’Académie des Sciences, Séance du 20 Janvier 1913, présentée par M. Appell (156): 203–205 
  • Bachelier, L. (1914), Le Jeu, la Chance et le Hasard, Bibliothèque de Philosophie scientifique, E. Flammarion 
  • Bachelier, L. (1920a), Sur la théorie des corrélations, Bulletin de la Société Mathématique de France. Vie de la société. Comptes rendus des Séances, Séance du 7 Juillet 1920 (48): 42–44 
  • Bachelier, L. (1920b), Sur les décimales du nombre {\pi}, Bulletin de la Société Mathématique de France. Vie de la société. Comptes rendus des Séances, Séance du 7 Juillet 1920 (48): 44–46 
  • Bachelier, L. (1937), Les lois des grands nombres du Calcul des Probabilités, Gauthier-Villars 
  • Bachelier, L. (1938), La spéculation et le Calcul des Probabilités, Gauthier-Villars 
  • Bachelier, L. (1939), Les nouvelles méthodes du Calcul des Probabilités, Gauthier-Villars 
  • Bachelier, L. (1992), Reprint of Calcul des probabilités (1912) 1, Editions Jacques Gabay, ISBN 2-87647-090-X 
  • Bachelier, L. (1993), Reprint of Le Jeu, la Chance et le Hasard (1914), Editions Jacques Gabay, ISBN 2-87647-147-7 
  • Bachelier, L. (1995), Combined volume prints of Théorie de la spéculation (1900b) and Théorie mathématique du jeu (1901), Editions Jacques Gabay, ISBN 2-87647-129-9 
  • Cootner, P.H. (ed.) (1964), The Random Character of Stock Market Prices, Cambridge, MA: MIT Press 

External links[edit]