Abstract
In 1900, the mathematician Louis Bachelier proposed in his dissertation “Théorie de la Spéculation” to model the dynamics of stock prices as an arithmetic Brownian motion (the mathematical definition of Brownian motion had not yet been given by N. Wiener) and provided for the first time the exact definition of an option as a financial instrument fully described by its terminal value. In his 1965 paper “Theory of Rational Warrant Pricing”, the economist and Nobel prize winner Paul Samuelson, giving full recognition to Bachelier’s fondamental contribution, transformed the arithmetic Brownian motion into a geometric Brownian motion assumption to account for the fact that stock prices cannot take negative values.
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Geman, H. (2001). Functionals of Brownian Motion in Finance and in Insurance. In: Exponential Functionals of Brownian Motion and Related Processes. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56634-9_1
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DOI: https://doi.org/10.1007/978-3-642-56634-9_1
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