Aspects of Mathematical Finance

Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Acadmie 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 "Acadmie 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 Lvy processes. The Ariadnes thread leads the reader from Louis Bacheliers thesis 1900 to the famous Black-Scholes formula of 1973 and to most recent work close to Malliavins 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.