Aspects of Mathematical Finance

ISBN-13: 9783540752585 / Angielski / Twarda / 2008 / 80 str.

Marc Yor; K. Qechar; M. Yor

Opis

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 "Academie 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 "Academie 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 Levy 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."

Spis treści

Introduction: Some Aspects of Mathematical Finance (Marc Yor). -Financial Uncertainty, Risk Measures and Strong Preferences (Hans Föllmer). -The Notion of Arbitrage and Free Lunch in Mathematical Finance (Walter Schachermayer). -Dynamic Financial Risk Management (Pauline Barrieu and Nicole El Karoui). -Stochastic Clock and Financial Markets (Hélyette Geman). -Options and Partial Differential Equations (Damien Lamberton). -Mathematics and Finance (Émmanuel Gobet, Gilles Pagès, Marc Yor).

Blurb

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.