Nonlinear Expectations and Stochastic Calc...

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Beschreibung

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 den Autor

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).

Zusammenfassung

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

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2019
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xiii 212 S. 10 s/w Illustr. 212 p. 10 illus.
ISBN-13:	9783662599020
ISBN-10:	3662599023
Sprache:	Englisch
Einband:	Gebunden
Autor:	Peng, Shige
Auflage:	1st edition 2019
Hersteller:	Springer Berlin Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 18 mm
Von/Mit:	Shige Peng
Erscheinungsdatum:	19.09.2019
Gewicht:	0,512 kg