Optional Processes

Theory and Applications
1. Auflage 2020
ISBN: 978-1-138-33726-8
Verlag: Chapman and Hall/CRC

Buch, Englisch, 392 Seiten, Format (B × H): 196 mm x 241 mm, Gewicht: 927 g

Reihe: Chapman and Hall/CRC Financial Mathematics Series

It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications.

Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis.

This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance.

Features

- Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas

- Compiles almost all essential results on the calculus of optional processes in unusual probability spaces

- Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes

- Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism, etc.

Zielgruppe

Professional Practice & Development

Autoren/Hrsg.

Abdelghani, Mohamed

Melnikov, Alexander

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik
• Wirtschaftswissenschaften Finanzsektor & Finanzdienstleistungen Finanzsektor & Finanzdienstleistungen: Allgemeines

Inhaltsverzeichnis

1. Spaces, Laws and Limits. 2. Stochastic Processes. 3. Martingales. 4. Strong Supermartingales. 5. Optional Martingales. 6. Optional Supermartingales Decomposition. 7. Calculus of Optional Semimartingales. 8. Optional Stochastic Equations. 9. Optional Financial Markets. 10. Defaultable Markets on Unusual Space. 11. Filtering of Optional Semimartingales. Bibliography. Index.

Über Autor(innen)

Mohamed Abdelghani completed his PhD in Mathematical Finance from the University of Alberta. He is currently working as a V.P. in quantitative finance and machine learning at Morgan Stanley, New York, USA.

Alexander Melnikov is a Professor in Mathematical Finance at the University of Alberta, Edmonton, Canada. His research interests belong to the area of contemporary stochastic analysis and its numerous applications in Mathematical Finance, Statistics and Actuarial Science. He has written six books as well as over one hundred research papers in leading academic journals.