Mathematical Finance : Asset Pricing

The Bachelier World Congress has been organized every two years by the Bachelier Finance Society since 2000. This conference is a must-attend meeting place for leading specialists in financial mathematics. It bears the name of Louis Bachelier, a French mathematician who is credited with the birth of a new field of mathematics, applied to finance, by introducing random walks to model prices, even before the mathematical foundations of probability theory had been definitively laid. However, before Bachelier, it seems that Jules Regnault, a stockbroker on the Paris Bourse, was the first to propose modeling price variations using random walks in his work Calculation of chances and philosophy of the award (see ).

March 29, 1900, Louis Bachelier defended his doctoral thesis, supervised by Henri Poincaré. The originality of his work lies in the use of Brownian motion for the first time to model variations in the price of a financial asset. Brownian motion takes its name from a Scottish botanist, Richard Brown, who observed the agitation of pollen particles suspended in water. A little later, in 1905, Einstein and Jean Perrin use Brownian motion to estimate the Avogadro number .

American mathematician Norbert Wiener who, between 1920 and 1924, gave a rigorous mathematical definition to the mathematical object of Brownian motion, also known as the Wiener process. It is a law (of random variables) whose possible values are continuous trajectories. ${\left(W_t\right)}_{t\in \left[0,\infty \right)}$...