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Financial markets, ruling both industrial and commercial development, dominate today's economies. The mathematics that supports the financial markets is what the economy depends on as a whole; mathematical formulae underlay the functions of major banks. This translation of the prize-winning French original shows how the application of mathematics to finance has turned the latter into an exact science as well as formidable and efficient tool. The author, Nicolas Bouleau, is a professor at l'Ecole des Ponts-et-Chaussées and a director of one of the first French research groups to work with banks and financial derivatives.