Mathematical Finance, Vol. 10, No. 3 (July 2000), 341–353LOUIS BACHELIERON THE CENTENARY OF TH´EORIE DE LA SP´ECULATION∗Jean-Michel CourtaultL.I.B.R.E., Facult´e de Droit et de Sciences Economiques, Universite de Franche-Comte,45 D, Avenue de l’Observatoire, 25030 Besan¸con Cedex, FranceYuri KabanovLaboratoire de Math´ematiques, Universit´e de Franche-Comt´e, 16 Route de Gray,25030 Besan¸con Cedex, FranceBernard BruUniversit´e de Paris 45, rue des Saint-P`eres, 75005 Paris, FrancePierre Cr´epelAnalyse Num´erique, Bˆatiment 101, Universit´e Claude Bernard—Lyon I,43, Bd du 11 Novembre 1918, 69622 Villeurbanne Cedex, FranceIsabelle Lebon and Arnaud Le MarchandUniversit´e du Havre, Facult´e des Affaires, Internationales, D´epartement AES—SciencesEconomiques, 25 rue Philippe Lebon BP 420, 76057 Le Havre Cedex, France1. CENTENARY OF MATHEMATICAL FINANCEThe date March 29, 1900, should be considered as the birthdate of mathematical finance.On that day, a French postgraduate student, Louis Bachelier, successfully defended atthe Sorbonne his thesis Th´eorie de la Sp´eculation. As a work of exceptional merit,strongly supported by Henri Poincar´e, Bachelier’s supervisor, it was published in AnnalesScientifiques de l’´Ecole Normale Sup´erieure, one of the most influential French scientificjournals.This pioneering analysis of the stock and option markets contains several ideas ofenormous value in both finance and probability. In particular, the theory of Brownianmotion, one of the most important mathematical discoveries of the twentieth century, wasinitiated and used for the mathematical modeling of price movements and the evaluationof contingent claims in financial markets.The thesis of Louis Bachelier, together with his subsequent works, deeply influencedthe whole development of stochastic calculus and mathematical finance. As a testimonyof his great contribution, the newly created international Bachelier Finance Society isnamed after him. The centenary of the famous thesis is widely celebrated as a landmarkAddress correspondence to Y. Kabanov, Laboratoire de Math´ematiques, Universit´e de Franche-Comt´e,16 Route de Gray, 25030 Besan¸con Cedex, France; e-mail: [email protected].∗We would like to thank C´ecile Bachelier-de Visme, Odile Larive, Hˆel´ene Nocton, and M. Rolland. Thispaper is dedicated to the memory of C´ecile Bachelier-de Visme.© 2000 Blackwell Publishers, 350 Main St., Malden, MA 02148, USA, and 108 Cowley Road, Oxford,OX4 1JF, UK.341342 j.-m. courtault et al.event in the history of modern science. On this occasion we present to the readers’attention a brief account of our research on Louis Bachelier. In spite of his remarkablecontributions, he remained in obscurity for decades—one of the most mysterious figuresin mathematics of the twentieth century, about whom only a few facts could be found inthe literature. Recently there has been enormous public interest in his scientific biography,resulting from the amazingly fast development of mathematical finance in the last twodecades and a deeper understanding of the fundamental role of Brownian motion.We believe that our short note brings some new light on Louis Bachelier, as a person,a mathematician, and a philosopher.11 March 1870 Louis Jean-Baptiste Alphonse Bachelier is born in Le HavreOctober 1888 Graduates from secondary school at Caen11 January 1889 Father’s death7 May 1889 Mother’s death1889–1891 Bachelier is the head of Bachelier fils1891–1892 Military service1892 Student at SorbonneOctober 1895 Bachelor in sciences at SorbonneJuly 1897 Certificate in mathematical physics29 March 1900 Bachelier defends his thesis, Th´eorie de la Sp´eculation1909–1914 Free lecturer at Sorbonne1912 Publication of Calcul des Probabilit´es1914 Publication of Le Jeu, la Chance et le Hasard9 September 1914 Drafted as a private in the French army31 December 1918 Back from the army10 December 1919 A member of the French Mathematical Society1919–1922 Assistant professor in Besan¸con14 September 1920 Marries Augustine Jeanne Maillot; she died soon1922–1925 Assistant professor in Dijon1925–1927 Associate professor in RennesJanuary 1926 Blackballed in Dijon1 October 1927 Professor in Besan¸con1937 Professor Emeritus1 October 1937 Retirement1941 The last publication28 April 1946 Louis Bachelier dies in Saint-Servan-sur-Mer; and is buried inSanvic near Le Havre1996 The Bachelier Finance Society is founded2. BACHELIER’S EARLY YEARSLouis Bachelier was born into a respected bourgeois family known in Le Havre forits cultural and social traditions. His father, Alphonse Bachelier, was not only a winemerchant but also the vice-consul of Venezuela at Le Havre and an amateur scientist. Hismother, Cecile Fort-Meu, was a banker’s daughter; his grandfather, an important personin the financial business, was known also as the author of poetry books. Unfortunately,just after Louis graduated from the secondary school at Caen, earning the French bachelorth´eorie de la sp´eculation 343degree baccalaur´eat es sciences, his parents died and he had to interrupt his studies tocontinue his father’s business and take care of his sister and three-year-old brother.This dramatic event had far-reaching consequences for his academic career; in par-ticular, they explain why Bachelier did not follow any grande ´ecole with the Frenchscientific elite, a weak point in his curriculum. Nevertheless, as the head of the familyenterprise (officially registered as Bachelier fils) he became acquainted with the worldof financial markets, and one can find some hints of personal experiences in his works.Military service soon followed, bringing further delay of his studies (an enormoushandicap in a forming mathematician!). Finally, in 1892 Louis arrived in Paris to continuehis university education at the Sorbonne. Scarce information is available about theseyears, though it is known that he followed lectures of Paul Appell, Joseph Boussinesq,and Henri Poincar´e and that, apparently, he was not among the best students (his marksin mathematics in the 1895 register were largely below those of his classmates Langevinand Li´enard). But in spite of the four-year interruption, Bachelier’s development as ascientist was fast enough and he wrote his celebrated thesis, Th´eorie de la Sp´eculation,on the application of probability to stock markets. This was historically the first attemptto use