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.