# Louis Bachelier

Louis Jean-Baptiste Alphonse Bachelier (French: [baʃəlje]; 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, as part of his PhD thesis The Theory of Speculation (Théorie de la spéculation, published 1900).

Bachelier’s Doctoral thesis, which introduced for the first time a mathematical model of Brownian motion and its use for valuing stock options, is historically the first paper to use advanced mathematics in the study of finance. Thus, Bachelier is considered as the forefather of mathematical finance and a pioneer in the study of stochastic processes.

Louis Bachelier
Louis Bachelier, aged 15
Born March 11, 1870
Died April 28, 1946 (aged 76)
Nationality French
Alma mater University of Paris
Known for Pioneer in mathematical finance
Scientific career
Fields Mathematics
Institutions University of Paris
Université de Franche-Comté (Besançon)
Université de Dijon
University of Rennes
Influenced Benoit Mandelbrot, Paul Samuelson, Fischer Black, Myron Scholes

## Early years

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

Defended on March 29, 1900 at the University of Paris,[2] Bachelier's thesis was not well received because it attempted to apply mathematics to an unfamiliar area for mathematicians.[3] However, his instructor, Henri Poincaré, is recorded as having 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

very original, and all the more interesting in that Fourier's reasoning can be extended with a few changes to the theory of errors. ... It is regrettable that M. Bachelier did not develop this part of his thesis further.

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 Théorie de la spéculation" 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."

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.[4] In 1919, he found a position as an assistant professor in Besançon, replacing a regular professor on leave.[4] He married Augustine Jeanne Maillot in September 1920 but was soon widowed.[4] When the professor returned in 1922, Bachelier replaced another professor at Dijon.[4] He moved to Rennes in 1925, but was finally awarded a permanent professorship in 1927 at the University of Besançon, where he worked for 10 years until his retirement.[4]

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.[5]

Although Bachelier's work on random walks predated Einstein's celebrated study of Brownian motion by five years, the pioneering nature of his work was recognized only after several decades, first by Andrey Kolmogorov who pointed out his work to Paul Lévy, then by Leonard Jimmie Savage who translated Bachelier's thesis to English and brought the work of Bachelier to the attention of Paul Samuelson. Bachelier arguments used in his thesis also predate Eugene Fama's Efficient-market hypothesis, which is very closely related, as the idea of random walk is suited to predict the random future in a stock market where everyone has all the available information. His work in finance is recognized as one of the foundations for the Black–Scholes model.

## Works

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
Translated into English, Harding 2017
Erratum, Bachelier 1941b

## Citations

1. ^ Felix 1970, pp. 366–367
2. ^ https://www.encyclopediaofmath.org/images/f/f1/LouisBACHELIER.pdf
3. ^ Weatherall, James Owen (January 2, 2013). The Physics of Wall Street: A Brief History of Predicting the Unpredictable. Houghton Mifflin Harcourt. pp. 10–11. ISBN 978-0547317274.
4. 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.
5. ^ Mandelbrot, Benoit; Hudson, Richard L. (2014), The Misbehavior of Markets: A Fractal View of Financial Turbulence, Basic Books, pp. 48–49, ISBN 9780465004683.
6. ^ Rietz H. L. (1914). "Review: Calcul des Probabilités by Louis Bachelier. Tome I" (PDF). Bull. Amer. Math. Soc. 20 (5): 268–273. doi:10.1090/s0002-9904-1914-02484-x.

## References

• 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), pp. 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), pp. 42–44
• 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
• Bachelier, L.; Samuelson, P. A.; Davis, M.; Etheridge, A. (2006), Louis Bachelier's Theory of Speculation: the Origins of Modern Finance, Princeton NJ: Princeton University Press, ISBN 978-0-691-11752-2
• Cootner, P.H. (ed.) (1964), The Random Character of Stock Market Prices, Cambridge, MA: MIT Press