Stochastic Calculus and Applications

2. Auflage 2015
ISBN: 978-1-4939-2866-8
Verlag: Springer

Buch, Englisch, 666 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 11524 g

Reihe: Probability and Its Applications

Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry.

New features of this edition include:

End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index.

"Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."–Zentralblatt (from review of the First Edition)

Zielgruppe

Graduate

Autoren/Hrsg.

Elliott, Robert J.

Cohen, Samuel N.

Fachgebiete

• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

Part I: Measure Theoretic Probability.- Measure Integral.- Probabilities and Expectation.- Part II: Stochastic Processes.- Filtrations, Stopping Times and Stochastic Processes.- Martingales in Discrete Time.- Martingales in Continuous Time.- The Classification of Stopping Times.- The Progressive, Optional and Predicable -Algebras.- Part III: Stochastic Integration.- Processes of Finite Variation.- The Doob-Meyer Decomposition.- The Structure of Square Integrable Martingales.- Quadratic Variation and Semimartingales.- The Stochastic Integral.- Random Measures.- Part IV: Stochastic Differential Equations.- Ito's Differential Rule.- The Exponential Formula and Girsanov's Theorem.- Lipschitz Stochastic Differential Equations.- Markov Properties of SDEs.- Weak Solutions of SDEs.- Backward Stochastic Differential Equations.- Part V: Applications.- Control of a Single Jump.- Optimal Control of Drifts and Jump Rates.- Filtering. Part VI: Appendices.

Über Autor(innen)

Samuel N. Cohen is an Associate Professor in the Mathematical Institute at the University of Oxford, an associate member of the Oxford-Man Institute for Quantitative Finance and a member of the Oxford-Nie Financial Big Data Laboratory. He has a Ph.D. in Mathematics from the University of Adelaide, along with undergraduate degrees in Mathematics and Finance.

Robert Elliott received Bachelors and Masters degrees from Oxford University, and his Ph.D. and D.Sc. from the University of Cambridge. He has held positions at Newcastle, Yale, Oxford, Warwick, Hull, Alberta, Calgary and Adelaide, and visiting positions in Toronto, Northwestern, Kentucky, Brown, Paris, Denmark, Hong Kong and Australia. From 2001 to 2009 he was the RBC Financial Group Professor of Finance at the University of Calgary, Canada, where he was also an Adjunct Professor in both the Department of Mathematics and the Department of Electrical Engineering. From 2009 to 2013 he was an Australian Professorial Fellow atthe University of Adelaide. Professor Elliott has authored nine books and over 450 papers.