This book is taken from the lectures given at the ENSAE in March
1998 and at the Scuola Normale Superiore in May 1998. At the
beginning of the 70's, the set of mathematical methods of finance
were reduced to actuarial calculus. The modern approach uses the
stochastic calculus theory and evidences the duality between
problems of arbitrage and valorisation and a set of martingale
probabilities.
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