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    Home : Math Matters - A Brief Look at How Mathematics has Influenced Modern Life : Petroleum & Petrochemicals
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Petroleum & Petrochemicals

Robert Brown
(Scottish, 1773-1858)
is the botanist in honor of whom Brownian motion was named.
Louis Jean-Baptiste Alphonse Bachelier (French, 1870 - 1946) is credited with being the first person to model Brownian motion.
The importance of petroleum to the global economy cannot be overstated. The price of petroleum has a large impact on global growth, and in the long term, the greatest single factor influencing petroleum prices is the cost of crude oil. As such, its trading activity is closely watched and routinely scrutinized.

The first successful attempt to model speculative prices was made by Louis Bachelier in his 1900 Ph.D. thesis “The Theory of Speculation”. Bachelier used stochastic processes such as Brownian motion to model the market noise of the Paris Bourse.

Geometric Brownian Motion:

Where Xt is the price of an investment at time
t, with time measured in trading days from initial purchase, rXtdt is the size of the predicted change, sXtdt is the standard deviation and is the increment of Brownian motion.

Almost 65 years later, Bachelier’s ideas were taken up with significant effect by the Nobel prize-winning economist Paul Anthony Samuelson (American, 1915), who argued that discounted futures prices must fluctuate randomly. His work provided the basis of what is now known as the “efficient market hypothesis”, which caused a revolution in empirical finance.

Today, stochastic processes are used to model a wide range of things including stock prices, interest rates and commodity prices.