Louis Bachelier
Encyclopedia
Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 – April 28, 1946) 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.
. 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.
. 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 note of honorable, and was accepted for publication in the prestigious Annales Scientifiques de l’École Normale Supérieure. The fact that it did not receive a mark of très honorable, despite its ultimate importance, 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." Positive feedback from Poincaré can be attributed to the mathematician's interest in mathematical ideas, not just rigorous proof. "Poincare: un intuitif Character"
. In 1914, he published a book, Le Jeu, la Chance, et le Hasard (Games, Chance, and Risk), 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. After the war, he found a position in Besançon
, replacing a regular professor on leave. When the professor returned in 1922, Bachelier replaced another professor at Dijon
. He moved to Rennes
in 1925, but was finally awarded a permanent professorship in 1927 at Besançon, where he worked for 10 years.
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 Pierre 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 in 1931.
Also notable is that Bachelier's work on random walk
s was more mathematical and predated Einstein
's celebrated study of Brownian motion
by five years.
French people
The French are a nation that share a common French culture and speak the French language as a mother tongue. Historically, the French population are descended from peoples of Celtic, Latin and Germanic origin, and are today a mixture of several ethnic groups...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
at the turn of the 20th century. He is credited with being the first person to model the stochastic process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
now called Brownian motion
Brownian motion
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
, 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
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
. Thus, Bachelier is considered a pioneer in the study of financial mathematics and stochastic processes.
Early years
Bachelier was born in Le HavreLe Havre
Le Havre is a city in the Seine-Maritime department of the Haute-Normandie region in France. It is situated in north-western France, on the right bank of the mouth of the river Seine on the English Channel. Le Havre is the most populous commune in the Haute-Normandie region, although the total...
. His father was a wine
Wine
Wine is an alcoholic beverage, made of fermented fruit juice, usually from grapes. The natural chemical balance of grapes lets them ferment without the addition of sugars, acids, enzymes, or other nutrients. Grape wine is produced by fermenting crushed grapes using various types of yeast. Yeast...
merchant and amateur
Amateur
An amateur is generally considered a person attached to a particular pursuit, study, or science, without pay and often without formal training....
scientist
Scientist
A scientist in a broad sense is one engaging in a systematic activity to acquire knowledge. In a more restricted sense, a scientist is an individual who uses the scientific method. The person may be an expert in one or more areas of science. This article focuses on the more restricted use of the word...
, and the vice-consul of Venezuela
Venezuela
Venezuela , officially called the Bolivarian Republic of Venezuela , is a tropical country on the northern coast of South America. It borders Colombia to the west, Guyana to the east, and Brazil to the south...
at Le Havre. His mother was the daughter of an important banker (who was also a writer of poetry
Poetry
Poetry is a form of literary art in which language is used for its aesthetic and evocative qualities in addition to, or in lieu of, its apparent meaning...
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
Military
A military is an organization authorized by its greater society to use lethal force, usually including use of weapons, in defending its country by combating actual or perceived threats. The military may have additional functions of use to its greater society, such as advancing a political agenda e.g...
service. Bachelier arrived in Paris in 1892 to study at the Sorbonne
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
, where his grades were less than ideal.
The Thesis
Historians argue Bachelier's thesis was not appropriately received, resulting in Academia blackballingBlackball (blacklist)
Blackballing is a rejection in a traditional form of secret ballot, where a white ball or ballot constitutes a vote in support and a black ball signifies opposition. This system is typically used where a club's rules provide that, rather than a majority of the votes, one or two objections are...
. However, his instructor, Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
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
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
' law of errors
The thesis received a note of honorable, and was accepted for publication in the prestigious Annales Scientifiques de l’École Normale Supérieure. The fact that it did not receive a mark of très honorable, despite its ultimate importance, 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." Positive feedback from Poincaré can be attributed to the mathematician's interest in mathematical ideas, not just rigorous proof. "Poincare: un intuitif Character"
Academic career
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 SorbonneSorbonne
The Sorbonne is an edifice of the Latin Quarter, in Paris, France, which has been the historical house of the former University of Paris...
. In 1914, he published a book, Le Jeu, la Chance, et le Hasard (Games, Chance, and Risk), that sold over six thousand copies. With the support of the Council of the University of Paris
University of Paris
The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...
, Bachelier was given a permanent professorship at the Sorbonne, but World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
intervened and Bachelier was drafted into the French army as a private. After the war, he found a position in Besançon
Besançon
Besançon , is the capital and principal city of the Franche-Comté region in eastern France. It had a population of about 237,000 inhabitants in the metropolitan area in 2008...
, replacing a regular professor on leave. When the professor returned in 1922, Bachelier replaced another professor at Dijon
Dijon
Dijon is a city in eastern France, the capital of the Côte-d'Or département and of the Burgundy region.Dijon is the historical capital of the region of Burgundy. Population : 151,576 within the city limits; 250,516 for the greater Dijon area....
. He moved to Rennes
Rennes
Rennes is a city in the east of Brittany in northwestern France. Rennes is the capital of the region of Brittany, as well as the Ille-et-Vilaine department.-History:...
in 1925, but was finally awarded a permanent professorship in 1927 at Besançon, where he worked for 10 years.
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 Pierre Lévy
Paul Pierre Lévy
Paul Pierre Lévy was a Jewish French mathematician who was active especially in probability theory, introducing martingales and Lévy flights...
, 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 in 1931.
Also notable is that Bachelier's work on random walk
Random walk
A random walk, sometimes denoted RW, is a mathematical formalisation of a trajectory that consists of taking successive random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the...
s was more mathematical and predated Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
's celebrated study of Brownian motion
Brownian motion
Brownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
by five years.
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, , 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
- MartingaleMartingale (probability theory)In probability theory, a martingale is a model of a fair game where no knowledge of past events can help to predict future winnings. In particular, a martingale is a sequence of random variables for which, at a particular time in the realized sequence, the expectation of the next value in the...
- Random walkRandom walkA random walk, sometimes denoted RW, is a mathematical formalisation of a trajectory that consists of taking successive random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the...
- Brownian MotionBrownian motionBrownian motion or pedesis is the presumably random drifting of particles suspended in a fluid or the mathematical model used to describe such random movements, which is often called a particle theory.The mathematical model of Brownian motion has several real-world applications...
- Henri PoincaréHenri PoincaréJules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
External links
- "Bachelier Finance Society"
- "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
- Bachelier's theory of speculation is demonstrated by this 8 ft tall Probability Machine comparing stock market returns to the randomness of the beans dropping through the quincunx pattern. also from Index Funds Advisors, this discussion of Bachelier's and other academic's contribution to financial science.