Mathematical Methods for Financial Markets

Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes.

The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.

List of contents

Continuous Path Processes.- Continuous-Path Random Processes: Mathematical Prerequisites.- Basic Concepts and Examples in Finance.- Hitting Times: A Mix of Mathematics and Finance.- Complements on Brownian Motion.- Complements on Continuous Path Processes.- A Special Family of Diffusions: Bessel Processes.- Jump Processes.- Default Risk: An Enlargement of Filtration Approach.- Poisson Processes and Ruin Theory.- General Processes: Mathematical Facts.- Mixed Processes.- Lévy Processes.

About the author

Marc Chesney, Professor für Quantitative Finance an der Universität Zürich, vertritt einen kritischen Standpunkt gegenüber der Finanzbranche. Er ist Autor verschiedener Artikel im Bereich der Gefahren, die mit der Größe und Komplexität der Finanzsphäre verbunden sind. Marc Chesney ist Mitglied von "Finance Watch" und "Kontrapunkt". Er war Research Fellow am "Zentrum für Religion, Wirtschaft und Politik" (Collegium Helveticum) und ist heute Mitglied der "Trägerversammlung des ZRWP".

Summary

Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes.

The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.

Additional text

concepts of continuous-time finance … . This text presents an up-to-date account of the powerful interplay between the two areas, which is accessible yet mathematically rigorous. … This book is an accessible overview of the relevant sophisticated topics in the theory of processes, serves as an excellent guide through the literature and will doubtless become established as a standard work of reference for practitioners and researchers in the area of mathematical finance.” (Aleksandar Mijatović, Mathematical Reviews, Issue 2011 h)
“Mathematical Methods for Financial Markets succeeds to be both an excellent finance textbook and an excellent maths textbook. … the work examined here is an excellent reading, going well beyond the Hull, that should be advised to all serious students in quantitative finance, and perhaps to a few colleagues who would want to enlarge their filtration about this topic. This is a prodigious encyclopaedia designed by the best authors in the field.” (Olivier Le Courtois, Revue de l'Association Française de Finance, Vol. 31 (1), 2010)

Report

concepts of continuous-time finance ... . This text presents an up-to-date account of the powerful interplay between the two areas, which is accessible yet mathematically rigorous. ... This book is an accessible overview of the relevant sophisticated topics in the theory of processes, serves as an excellent guide through the literature and will doubtless become established as a standard work of reference for practitioners and researchers in the area of mathematical finance." (Aleksandar Mijatovic, Mathematical Reviews, Issue 2011 h)
"Mathematical Methods for Financial Markets succeeds to be both an excellent finance textbook and an excellent maths textbook. ... the work examined here is an excellent reading, going well beyond the Hull, that should be advised to all serious students in quantitative finance, and perhaps to a few colleagues who would want to enlarge their filtration about this topic. This is a prodigious encyclopaedia designed by the best authors in the field." (Olivier Le Courtois, Revue de l'Association Française de Finance, Vol. 31 (1), 2010)

Product details

• Authors: Marc Chesney, Moniqu Jeanblanc, Monique Jeanblanc, Mar Yor, Marc Yor
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 15.10.2009
• EAN: 9781852333768
• ISBN: 978-1-85233-376-8
• No. of pages: 732
• Dimensions: 160 mm x 46 mm x 240 mm
• Weight: 1286 g
• Illustrations: XXVI, 732 p. 9 illus.
• Series: Springer Finance; Textbook; Springer Finance Textbooks; Springer Finance; Springer Finance Textbooks; Textbook
• Subject: Social sciences, law, business > Business > General, dictionaries