Table of contents
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.
- Book Title Nonlinear Expectations and Stochastic Calculus under Uncertainty
- Book Subtitle with Robust CLT and G-Brownian Motion
- Series Title Probability Theory and Stochastic Modelling
- Series Abbreviated Title Probability and Stochastic (formerly: PIA & SMAP)
- DOI https://doi.org/10.1007/978-3-662-59903-7
- Copyright Information Springer-Verlag GmbH Germany, part of Springer Nature 2019
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-3-662-59902-0
- Softcover ISBN 978-3-662-59905-1
- eBook ISBN 978-3-662-59903-7
- Series ISSN 2199-3130
- Series E-ISSN 2199-3149
- Edition Number 1
- Number of Pages XIII, 212
- Number of Illustrations 10 b/w illustrations, 0 illustrations in colour
Probability Theory and Stochastic Processes
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