Mathematical Methods for Financial Markets

Stochastic processes of common use in mathematical finance are presented in this book, which interlaces financial concepts and instruments such as arbitrage opportunities, option pricing and default risk with Brownian motion and Lévy and diffusion processes. This book interlaces financial concepts and instruments, such as arbitrage opportunities, admissible strategies, contingent claims, option pricing, default risk, ruin, with Brownian motion, diffusion processes, Lévy processes, together with the basic properties of these processes. The first half of the book is devoted to continuous path processes while the second half covers discontinuous processes. Assuming only basic knowledge of probability theory, the book is organized so that the mathematical facts pertaining to a given financial question are gathered close to the study of that question.

Unlike other texts available in the field, this book is written to be accessible to both mathematicians and practitioners

Rather than provide full proofs throughout, the authors give the essence of the argument and then refer readers to the literature whenever the discussion might become too technical.

Autorentext
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".

Inhalt
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.