Mathematical Methods for Financial Markets

From the reviews: "Mathematical Methods for Financial Markets provides a comprehensive overview of mathematical research inspired by financial markets, primarily derivative-securities markets. ... Mathematicians interested in finance who are trained in the theory of stochastic processes can find much of interest here." (John Curran, MAA Reviews, July, 2013) "The goal of the authors is to present the financial methodology and the relevant tools from mathematical stochastics. ... book is well structured and carefully written. The text is smooth and clear. ... book should be read, used and referred to on any occasion. ... a source of real intellectual pleasure and inspiration for further work. The book will be useful for a wide audience, from graduate and postgraduate students to researchers in stochastics and finance, as well as to applied scientists in other areas." (Jordan M. Stoyanov, Zentralblatt MATH, Vol. 1205, 2011) "The aim of this book is to explain the fundamental 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 Francaise de Finance, Vol. 31 (1), 2010)

• 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.