Stochastic processes of common use in mathematical finance are presented throughout this book, which consists of eleven chapters, interlacing on the one hand financial concepts and instruments, such as arbitrage opportunities, admissible strategies, contingent claims, option pricing, default risk, ruin, and onthe other hand, 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 whereas the second half deals with discontinuous processes. Only basic knowledge of probability theory is assumed; 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 can be easily comprehended by both mathematicians and practitioners When the discussion becomes technical, either in the direction of Mathematics or Finance, only the essence of the argument is given, along with references for the reader to approach in their own time INDICE: Part I 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. Part II: Jump Processes. Default Risk: An Enlargement of Filtration Approach.- Poisson Processes and Ruin Theory.- General Processes: Mathematical Facts.- Mixed Processes.- Lévy Processes.- Appendices.
- ISBN: 978-1-85233-376-8
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 755
- Fecha Publicación: 01/03/2009
- Nº Volúmenes: 1
- Idioma: Inglés