Considering the stupendous gain in importance in the banking and insurance industries since
the early 1990's of mathematical methodology especially probabilistic methodology it was a
very natural idea for the French Académie des Sciences to propose a series of public lectures
accessible to an educated audience to promote a wider understanding for some of the
fundamental ideas techniques and new tools of the financial industries. These lectures were
given at the Académie des Sciences in Paris by internationally renowned experts in mathematical
finance and later written up for this volume which develops in simple yet rigorous terms
some challenging topics such as risk measures the notion of arbitrage dynamic models
involving fundamental stochastic processes like Brownian motion and Lévy processes. The
Ariadne's thread leads the reader from Louis Bachelier's thesis 1900 to the famous
Black-Scholes formula of 1973 and to most recent work close to Malliavin's stochastic calculus
of variations. The book also features a description of the trainings of French financial
analysts which will help them to become experts in these fast evolving mathematical techniques.
