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Louis Jean-Baptiste Alphonse Bachelier (; 11 March 1870 – 28 April 1946) was a French
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
at the turn of the 20th century. He is credited with being the first person to model the
stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
now called Brownian motion, as part of his doctoral thesis ''The Theory of Speculation'' (''Théorie de la spéculation'', defended in 1900). Bachelier's doctoral thesis, which introduced the first mathematical model of Brownian motion and its use for valuing stock options, was the first paper to use advanced mathematics in the study of
finance Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of fina ...
. His
Bachelier model The Bachelier model is a model of an asset price under brownian motion presented by Louis Bachelier on his PhD thesis ''The Theory of Speculation'' (''Théorie de la spéculation'', published 1900). It is also called "Normal Model" equivalently (as ...
has been influential in the development of other widely used models, including the Black-Scholes model. Thus, Bachelier is considered as the forefather of
mathematical finance Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...
and a pioneer in the study of stochastic processes.


Early years

Bachelier was born in
Le Havre Le Havre (, ; nrf, Lé Hâvre ) is a port city in the Seine-Maritime department in the Normandy region of northern France. It is situated on the right bank of the estuary of the river Seine on the Channel southwest of the Pays de Caux, very cl ...
. His father was a
wine Wine is an alcoholic drink typically made from fermented grapes. Yeast consumes the sugar in the grapes and converts it to ethanol and carbon dioxide, releasing heat in the process. Different varieties of grapes and strains of yeasts are m ...
merchant and
amateur An amateur () is generally considered a person who pursues an avocation independent from their source of income. Amateurs and their pursuits are also described as popular, informal, autodidacticism, self-taught, user-generated, do it yourself, DI ...
scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, ...
, and the vice-consul of
Venezuela Venezuela (; ), officially the Bolivarian Republic of Venezuela ( es, link=no, República Bolivariana de Venezuela), is a country on the northern coast of South America, consisting of a continental landmass and many islands and islets in th ...
at Le Havre. His mother was the daughter of an important banker (who was also a writer of
poetry Poetry (derived from the Greek ''poiesis'', "making"), also called verse, is a form of literature that uses aesthetic and often rhythmic qualities of language − such as phonaesthetics, sound symbolism, and metre − to evoke meanings i ...
books). Both of Louis's 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 A military, also known collectively as armed forces, is a heavily armed, highly organized force primarily intended for warfare. It is typically authorized and maintained by a sovereign state, with its members identifiable by their distinct ...
service. Bachelier arrived in Paris in 1892 to study at the Sorbonne, where his grades were less than ideal.


The doctoral thesis

Defended on 29 March 1900 at the University of Paris, Bachelier's thesis was not well received because it attempted to apply mathematics to an area mathematicians found unfamiliar. However, his instructor,
Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
, is recorded as having given some positive feedback (though insufficient to secure Bachelier 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 Jean-Michel is a French masculine given name. It may refer to : * Jean-Michel Arnold, General Secretary of the Cinémathèque Française * Jean-Michel Atlan (1913–1960), French artist * Jean-Michel Aulas (born 1949), French businessman * Jean-Mi ...
et al. point out i
"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."


Academic career

For several years following the successful defense of his thesis, Bachelier further developed the theory of
diffusion processes Molecular diffusion, often simply called diffusion, is the thermal motion of all (liquid or gas) particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size (mass) of ...
, 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 , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...
, Bachelier was given a permanent professorship at the Sorbonne, but
World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
intervened and he was drafted into the French army as a private. His army service ended on December 31, 1918. In 1919, he found a position as an assistant professor in Besançon, replacing a regular professor on leave. He married Augustine Jeanne Maillot in September 1920 but was soon widowed. When the professor returned in 1922, Bachelier replaced another professor at
Dijon Dijon (, , ) (dated) * it, Digione * la, Diviō or * lmo, Digion is the prefecture of the Côte-d'Or department and of the Bourgogne-Franche-Comté region in northeastern France. the commune had a population of 156,920. The earlies ...
. He moved to
Rennes Rennes (; br, Roazhon ; Gallo: ''Resnn''; ) is a city in the east of Brittany in northwestern France at the confluence of the Ille and the Vilaine. Rennes is the prefecture of the region of Brittany, as well as the Ille-et-Vilaine department ...
in 1925, but was finally awarded a permanent professorship in 1927 at the
University of Besançon A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, t ...
, where he worked for 10 years until his retirement. 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. Although Bachelier's work on
random walk In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...
s predated
Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
'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 Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...
who pointed out his work to Paul Lévy, then by Leonard Jimmie Savage who translated Bachelier's thesis into English and brought the work of Bachelier to the attention of Paul Samuelson. The arguments Bachelier used in his thesis also predate Eugene Fama's efficient-market hypothesis, which is very closely related, as the idea of a 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

*, ''Théorie de la spéculation'' :Also published as a book, :Republished in a book of combined works, :Translated into English, :Translated into English with additional commentary and background, :Translated into English, *, ''Théorie mathématique du jeu'' :Republished in a book of combined works, *, ''Théorie des probabilités continues'' *, ''Étude sur les probabilités des causes'' *, ''Le problème général des probabilités dans les épreuves répétées'' *, ''Les probabilités à plusieurs variables'' *, ''Mouvement d’un point ou d’un système matériel soumis à l’action de forces dépendant du hasard'' *, (Book) ''Calcul des probabilités'' :Republished, *, ''Les probabilités cinématiques et dynamiques'' *, ''Les probabilités semi-uniformes'' *, (Book) ''Le Jeu, la Chance et le Hasard'' :Republished, :Translated into English
Harding 2017
*, ''La périodicité du hasard'' *, ''Sur la théorie des corrélations'' *, ''Sur les décimales du nombre '' *, ''Le problème général de la statistique discontinue'' *, ''Quelques curiosités paradoxales du calcul des probabilités'' *, (Book) ''Les lois des grands nombres du Calcul des Probabilités'' (Book) *, (Book) ''La spéculation et le Calcul des Probabilités'' *, (Book) ''Les nouvelles méthodes du Calcul des Probabilités'' *, ''Probabilités des oscillations maxima'' :Erratum,


See also

*
Black–Scholes equation In mathematical finance, the Black–Scholes equation is a partial differential equation (PDE) governing the price evolution of a European call or European put under the Black–Scholes model. Broadly speaking, the term may refer to a similar PDE ...
*
Bachelier model The Bachelier model is a model of an asset price under brownian motion presented by Louis Bachelier on his PhD thesis ''The Theory of Speculation'' (''Théorie de la spéculation'', published 1900). It is also called "Normal Model" equivalently (as ...
* Martingale *
Random walk In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...
* Brownian Motion *
Louis Bachelier Prize The Louis Bachelier Prize is a biennial prize in applied mathematics jointly awarded by the London Mathematical Society, the Natixis Foundation for Quantitative Research and the Société de Mathématiques Appliquées et Industrielles (SMAI) in ...
*
Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
*
Vinzenz Bronzin Vinzenz Bronzin (1872 in Rovigno – 1970 in Trieste) was an Italian mathematics professor, known today for an early ("rediscovered") option pricing formula, similar to, and predating, the Black–Scholes 1973 formula; he also provided a formula ...
*
Jules Regnault Jules Augustin Frédéric Regnault (; 1 February 1834, Béthencourt – 9 December 1894, Paris) was a French stock broker's assistant who first suggested a modern theory of stock price changes i''Calcul des Chances et Philosophie de la Bourse''( ...


Citations


References

*
Philip Ball Philip Ball (born 1962) is a British science writer. For over twenty years he has been an editor of the journal ''Nature'' for which he continues to write regularly. He now writes a regular column in '' Chemistry World''. He has contributed to ...
, ''Critical Mass'' Random House, 2004 , pp238–242. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


External links


"Louis Bachelier, fondateur de la finance mathématique"
Louis Bachelier webpage at the Université de Franche-Comté, Besançon / France. Text in French. * *
Louis Bachelier par Laurent Carraro et Pierre Crepel
*. also from Index Funds Advisors, this discussion o
Bachelier's and other academic's contribution to financial science.
{{DEFAULTSORT:Bachelier, Louis 19th-century French mathematicians 20th-century French mathematicians Probability theorists University of Paris alumni 1870 births 1946 deaths Scientists from Le Havre University of Burgundy alumni Chevaliers of the Légion d'honneur