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Home > Capital Markets Thinkers > Louis Bachelier

Capital Markets Thinkers

Louis Bachelier

The father of financial mathematics


Born in Le Havre, France.
Received a Bachelor in Sciences from the Sorbonne.
Received a Certificate in Mathematical Physics.
Publication of his PhD thesis, “The theory of speculation.”
Appointed lecturer at the Sorbonne.
Publication of Calcul des Probabilités.
Publication of Le Jeu, la Chance et le Hasard.
Drafted as a private into the French army.
Appointed assistant professor at University of Besançon.
Appointed assistant professor at University of Dijon.
Appointed associate professor at University of Rennes.
Appointed full professor at University of Besançon.
Appointed professor emeritus at University of Besançon.
Publication of Les Lois des Grands Nombres du Calcul des Probabilités.
Retired from academic life.
Publication of La Spéculation et le Calcul des Probabilités.
Publication of Les Nouvelles Méthodes du Calcul des Probabilités.
Died in Saint-Servan-sur-Mer, France.

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Life and Career

Louis Bachelier pioneered the study of financial mathematics well before it became central to financial practice. As a young man, he moved to Paris to study at the Sorbonne, where his doctoral thesis, The Theory of Speculation, helped originate the mathematics and modeling of finance, and the theory of Brownian motion. He was later offered a permanent professorship at the Sorbonne, with support from the Council of Paris University. However, he was unable to take up the position because World War I intervened and he was drafted into the French army. After the war he returned to academic life, and continued to research and write on financial mathematics, risk and probability. Public acknowledgement of his work, richly deserved for the innovations he brought to financial theory, did not really arrive until after his death, when he was rediscovered by those founding modern financial theory in the 1950s.

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Key Thinking

  • Bachelier is credited as the first person to model Brownian motion, as part of his thesis on The Theory of Speculation, to show that advanced mathematics could be used in the study of finance to evaluate stock options.

  • In mathematics, the Brownian motion is often referred to as the Wiener process, and Bachelier applied its simple stochastic process to modeling random fluctuations in stock prices.

  • His work on chance, probability and risk anticipated the random movements of financial market prices and has become an integral part of modern financial theory.

  • When he initially applied to join the University of Dijon he was rejected due to a misinterpretation of one of his papers by Paul Lévy, who appeared not to know of Bachelier or his work. Lévy later realized his error, and apologized to Bachelier.

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In Perspective

  • Bachelier’s successful defense of his thesis in 1900 marked the birth of mathematical finance, and it was later published in the influential French journal, Annales Scientifiques de l’Ecole Normale Supérieure.

  • His analysis of Brownian motion so that it could be applied to the mathematical modeling of price movements, and the evaluation of contingent claims in financial markets, is often thought of as one of the most important mathematical discoveries of the twentieth century.

  • His groundbreaking analysis of the stock and option markets included several key ideas for the development of both finance and probability.

  • Between 1900 and 1914, he developed the mathematical theory of diffusion processes in a series of papers published in reputed French journals.

  • In his book Le Jeu, la Chance et le Hasard, Bachelier considered the systematic use of the concept of continuity in probabilistic modeling.

  • He introduced many of the concepts of what later became stochastic analysis, in his attempt to find a theory for the valuation of financial options. His findings were similar to the work of Fischer Black, Myron Scholes, and Robert Merton in their seminal paper of 1973.

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“The mathematical expectation of the speculator is zero.”

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Further reading on Louis Bachelier


  • Bachelier, Louis. Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance. Princeton, NJ: Princeton University Press, 2006. This translation of Bachelier’s seminal work also contains a commentary on the development of stochastic analysis and financial economics.
  • Cootner, Paul H. (ed). The Random Character of Stock Market Prices. Cambridge, MA: MIT Press, 1964. A collection of research reprints on the randomness of the market up to 1964. It includes the first full English translation of Bachelier’s thesis, “The theory of speculation.”


  • Bachelier Finance Society, founded in 1996 by researchers in mathematical finance as a forum where academics and practitioners could exchange ideas and discuss their work:

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