Aspects of Mathematical Finance

• A collection of essays written by leading experts in the field of finance mathematics
• Based on lectures held on 1st February 2005 at the French Academy of Science

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.

The authors are: P. Barrieu, N. El Karoui, H. Föllmer, H. Geman, E. Gobet, G. Pagès, W. Schachermayer and M. Yor.

Table of contents (7 chapters)

• Introduction: Some Aspects of Financial Mathematics

  Pages 1-2

  Yor, Marc

• Financial Uncertainty, Risk Measures and Robust Preferences

  Pages 3-13

  Föllmer, Hans

• The Notion of Arbitrage and Free Lunch in Mathematical Finance

  Pages 15-22

  Schachermayer, Walter

• Dynamic Financial Risk Management

  Pages 23-35

  Barrieu, Pauline (et al.)

• Stochastic Clock and Financial Markets

  Pages 37-52

  Geman, Hèlyette

• Options and Partial Differential Equations

  Pages 53-61

  Lamberton, Damien

• Mathematics and Finance

  Pages 63-76

  Gobet, Emmanuel (et al.)

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