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This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included.
The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
About the author
Jianfeng Zhang is a professor of Mathematics at the University of Southern California, Los Angeles. His research interests include stochastic analysis, backward stochastic differential equations, stochastic numerics, and mathematical finance.
Summary
Provides a systematic study from linear equations to fully nonlinear equations
Includes up-to-date developments in the field
A powerful and convenient tool for financial engineering and stochastic optimization
Accessible to graduate students and junior researchers
Additional text
“This book (written by one of the leading experts in the field) constitutes a very handy and self-contained resource on BSDEs, both for people who want to get acquainted with the theory of BSDEs and Ph.D. students who aim to work in this field. … Overall the book is very well written and pleasant to read, and will likely become a classical reference on the topic.” (Anthony Réveillac, Mathematical Reviews, December, 2018)
“The book prefers clarity over generality in order to be more accessible and readable for the readers who are expected to be mainly Ph.D. students and junior researches in stochastic analysis.” (Martin Ondreját, zbMATH 1390.60004, 2018)
Report
"This book (written by one of the leading experts in the field) constitutes a very handy and self-contained resource on BSDEs, both for people who want to get acquainted with the theory of BSDEs and Ph.D. students who aim to work in this field. ... Overall the book is very well written and pleasant to read, and will likely become a classical reference on the topic." (Anthony Réveillac, Mathematical Reviews, December, 2018)
"The book prefers clarity over generality in order to be more accessible and readable for the readers who are expected to be mainly Ph.D. students and junior researches in stochastic analysis." (Martin Ondreját, zbMATH 1390.60004, 2018)
