Probability Theory and Stochastic Modelling

Nonlinear Expectations and Stochastic Calculus under Uncertainty

with Robust CLT and G-Brownian Motion

Autoren: Peng, Shige

Vorschau
  • Provides new notions and results of the theory of nonlinear expectations and related stochastic analysis
  • Summarizes the latest studies on G-Martingale representation theorem and Itô’s integrals
  • Includes exercises that help reader master and learn in each chapter
  •  
Weitere Vorteile

Dieses Buch kaufen

eBook 24,60 €
50,28 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
  • ISBN 978-3-662-59903-7
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF, EPUB
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 48,14 €
106,99 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
Softcover 32,09 €
64,19 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
Über dieses Buch

This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author.

This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes.

With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter.

Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.

Über die Autor*innen

Shige Peng received his PhD in 1985 at Université Paris-Dauphine, in the direction of mathematics and informatics, and 1986 at University of Provence, in the direction of applied mathematics. He now is a full professor in Shandong University. His main research interests are stochastic optimal controls, backward SDEs and the corresponding PDEs, stochastic HJB equations. He has received the Natural Science Prize of China (1995), Su Buqing Prize of Applied Mathematics (2006), TAN Kah Kee Science Award (2008), Loo-Keng Hua Mathematics Award (2011), and the Qiu Shi Award for Outstanding Scientists (2016).

Stimmen zum Buch

“The book is very interesting and useful for the specialists in stochastic calculus and its financial and other applications. It is written in a very clear language and therefore can be used for graduate students and practitioners. It presents very recent and modern subjects and so it will find a wide audience.” (Yuliya S. Mishura, zbMATH 1427.60004, 2020)

Inhaltsverzeichnis (8 Kapitel)

Inhaltsverzeichnis (8 Kapitel)
  • Sublinear Expectations and Risk Measures

    Seiten 3-21

    Peng, Shige

  • Law of Large Numbers and Central Limit Theorem Under Probability Uncertainty

    Seiten 23-45

    Peng, Shige

  • G-Brownian Motion and Itô’s Calculus

    Seiten 49-89

    Peng, Shige

  • G-Martingales and Jensen’s Inequality

    Seiten 91-100

    Peng, Shige

  • Stochastic Differential Equations

    Seiten 101-112

    Peng, Shige

Dieses Buch kaufen

eBook 24,60 €
50,28 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
  • ISBN 978-3-662-59903-7
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF, EPUB
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 48,14 €
106,99 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
Softcover 32,09 €
64,19 € (Listenpreis)
Preis für Deutschland (Brutto)
gültig bis 30. Juni 2021
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Bibliografische Information

Bibliographic Information
Buchtitel
Nonlinear Expectations and Stochastic Calculus under Uncertainty
Buchuntertitel
with Robust CLT and G-Brownian Motion
Autoren
Titel der Buchreihe
Probability Theory and Stochastic Modelling
Buchreihen Band
95
Copyright
2019
Verlag
Springer-Verlag Berlin Heidelberg
Copyright Inhaber
Springer-Verlag GmbH Germany, part of Springer Nature
eBook ISBN
978-3-662-59903-7
DOI
10.1007/978-3-662-59903-7
Hardcover ISBN
978-3-662-59902-0
Softcover ISBN
978-3-662-59905-1
Buchreihen ISSN
2199-3130
Auflage
1
Seitenzahl
XIII, 212
Anzahl der Bilder
10 schwarz-weiß Abbildungen
Themen