Nonlinear Expectations and Stochastic Calculus under Uncertainty

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).

“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)

• 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.