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Nonlinear Expectations and Stochastic Calculus under Uncertainty - with Robust CLT and G-Brownian Motion (Paperback, 1st ed. 2019)
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Nonlinear Expectations and Stochastic Calculus under Uncertainty - with Robust CLT and G-Brownian Motion (Paperback, 1st ed. 2019)
Series: Probability Theory and Stochastic Modelling, 95
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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.
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