# Louis Bachelier, the mathematician

In his thesis “**Theory of speculation**” (1900), the mathematician Louis Bachelier laid down the axiomatic bases of the long-term pricing of products, with an emphasis on two points:

- Trade can only take place if at a given moment buyers and sellers adopt the same “viewpoint” (probability law) on future price fluctuations.
- The principle of intertemporal price consistency is accepted by the market players.

From these he then deduced then that the distribution adopted by market players for the variation of prices could only be that of “**Brownian motion**”. The existence of a “**pricing**” probability distinct from statistical probability is central to Louis Bachelier’s thinking. These **original ideas** were used in the financial markets **after only their linkage to the idea of a hedging portfolio proposed by Black, Scholes and Merton in the 1970s**. Nevertheless, they opened the way to original mathematical developments, in particular the important idea of stochastic calculation, with very varied fields of application. These new tools made possible the effective use of the hedging portfolio.