Overview
- Content very comprehensive, at the same time well readable and motivated
- Suitable for advanced students as accompanying and further reading
- Suitable for lecturers as a basis for their own courses
Part of the book series: Mathematics Study Resources (MSR, volume 1)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
Keywords
- Option valuation in complete and incomplete markets
- Skorohods embedding theorem
- Donsker theorem
- Martingales and semi-martingales
- Stochastic integral
- Itô formula
- Stochastic analysis
- Option pricing
- Black-Scholes model
- Exponential levy models
- Optimal hedging strategies
- Portfolio optimization
- Utility optimization
About this book
Financial mathematical topics are first introduced in the context of discrete time processes and then transferred to continuous-time models. The basic construction of the stochastic integral and the associated martingale theory provide fundamental methods of the theory of stochastic processes for the construction of suitable stochastic models of financial mathematics, e.g. using stochastic differential equations. Central results of stochastic analysis such as the Itô formula, Girsanov's theorem and martingale representation theorems are of fundamental importance in financial mathematics, e.g. for the risk-neutral valuation formula (Black-Scholes formula) or the question of the hedgeability of options and the completeness of market models. Chapters on the valuation of options in complete and incomplete markets and on the determination of optimal hedging strategies conclude the range of topics.
Advanced knowledge of probability theory is assumed, in particular of discrete-time processes (martingales, Markov chains) and continuous-time processes (Brownian motion, Lévy processes, processes with independent increments, Markov processes). The book is thus suitable for advanced students as a companion reading and for instructors as a basis for their own courses.
This book is a translation of the original German 1st edition Stochastische Prozesse und Finanzmathematik by Ludger Rüschendorf, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com) and in a subsequent editing, improved by the author. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Stochastic Processes and Financial Mathematics
Authors: Ludger Rüschendorf
Series Title: Mathematics Study Resources
DOI: https://doi.org/10.1007/978-3-662-64711-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature 2023
Softcover ISBN: 978-3-662-64710-3Published: 05 April 2023
eBook ISBN: 978-3-662-64711-0Published: 04 April 2023
Series ISSN: 2731-3824
Series E-ISSN: 2731-3832
Edition Number: 1
Number of Pages: IX, 304
Number of Illustrations: 1 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Applications of Mathematics