Probability Theory and Stochastic Modelling

Nonlinear Expectations and Stochastic Calculus under Uncertainty

with Robust CLT and G-Brownian Motion

Authors: Peng, Shige

Free Preview
  • 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
  •  
see more benefits

Buy this book

eBook 24,60 €
50,28 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-662-59903-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 46,79 €
103,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-662-59902-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 31,19 €
62,39 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-662-59905-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

About the authors

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).

Reviews

“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)

Table of contents (8 chapters)

Table of contents (8 chapters)
  • Sublinear Expectations and Risk Measures

    Pages 3-21

    Peng, Shige

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

    Pages 23-45

    Peng, Shige

  • G-Brownian Motion and Itô’s Calculus

    Pages 49-89

    Peng, Shige

  • G-Martingales and Jensen’s Inequality

    Pages 91-100

    Peng, Shige

  • Stochastic Differential Equations

    Pages 101-112

    Peng, Shige

Buy this book

eBook 24,60 €
50,28 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-662-59903-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 46,79 €
103,99 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-662-59902-0
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 31,19 €
62,39 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-662-59905-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Nonlinear Expectations and Stochastic Calculus under Uncertainty
Book Subtitle
with Robust CLT and G-Brownian Motion
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
95
Copyright
2019
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
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
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XIII, 212
Number of Illustrations
10 b/w illustrations
Topics