Stochastic Processes and Financial Mathema...

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Beschreibung

The book provides an introduction to advanced topics in stochastic processes and related stochastic analysis, and combines them with a sound presentation of the fundamentals of financial mathematics. It is wide-ranging in content, while at the same time placing much emphasis on good readability, motivation, and explanation of the issues covered.

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 [...]) 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.

Über den Autor

Prof. Dr. Ludger Rüschendorf is professor at the University of Freiburg in the field of mathematical stochastics since 1993. Previously, he taught and conducted research at the universities of Hamburg, Aachen, Freiburg and Münster.

Zusammenfassung

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

Inhaltsverzeichnis

Option pricing in models in discrete time.- Scorohod's embedding theorem and Donsker's theorem.- Stochastic integration.- Elements of stochastic analysis.- Option pricing in complete and incomplete markets.- Utility optimization, minimum distance martingales, and utility indiff.- Variance-minimum hedging.

Details

Erscheinungsjahr:	2023
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	ix 304 S. 1 s/w Illustr. 304 p. 1 illus.
ISBN-13:	9783662647103
ISBN-10:	3662647109
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Rüschendorf, Ludger
Auflage:	1st edition 2023
Hersteller:	Springer Berlin Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 18 mm
Von/Mit:	Ludger Rüschendorf
Erscheinungsdatum:	05.04.2023
Gewicht:	0,482 kg

Artikel-ID: 120808201