Nonlinear Expectations and Stochastic Calculus under Uncertainty
Springer Berlin (Verlag)
978-3-662-59905-1 (ISBN)
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.
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.
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).
Sublinear Expectations and Risk Measures.- Law of Large Numbers and Central Limit Theorem under Uncertainty.- G-Brownian Motion and Itô's Calculus.- G-Martingales and Jensen's Inequality.- Stochastic Differential Equations.- Capacity and Quasi-Surely Analysis for G-Brownian Paths.- G-Martingale Representation Theorem.- Some Further Results of Itô's Calculus.- Appendix A Preliminaries in Functional Analysis.- Appendix B Preliminaries in Probability Theory.- Appendix C Solutions of Parabolic Partial Differential Equation.- Bibliography.- Index of Symbols.- Subject Index.- Author Index.
"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)
“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)
| Erscheinungsdatum | 05.03.2022 |
|---|---|
| Reihe/Serie | Probability Theory and Stochastic Modelling |
| Zusatzinfo | XIII, 212 p. 10 illus. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 355 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Wirtschaft ► Betriebswirtschaft / Management | |
| Schlagworte | central limit theorem • G-Brownian motion • G-martingale • G-martingale representation theorem • G-normal distribution • independence and identical distribution under uncertainty • law of large numbers • Mathematical Statistics • maximal distribution • nonlinear expectations • nonlinear Feynman-Kac formula • Probability Theory • quadratic variation process of G-Brownian motion • Quantitative Finance • stochastic analysis • stochastic differential equations driven by G-Brownian motion • stochastic integral of G-Brownian motion • uncertainty of probabilities |
| ISBN-10 | 3-662-59905-8 / 3662599058 |
| ISBN-13 | 978-3-662-59905-1 / 9783662599051 |
| Zustand | Neuware |
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