Backward Stochastic Differential Equations: From Linear to Fully Nonlinear Theory

by Jianfeng Zhang

Overview

This book provides a systematic and accessible approach to shastic differential equations, backward shastic 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 shastic 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 shastic analysis. It is also accessible for graduate students majoring in financial engineering.

Product Details

ISBN-13:	9781493972548
Publisher:	Springer New York
Publication date:	08/22/2017
Series:	Probability Theory and Stochastic Modelling , #86
Edition description:	1st ed. 2017
Pages:	388
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Jianfeng Zhang is a professor of Mathematics at the University of Southern California, Los Angeles. His research interests include shastic analysis, backward shastic differential equations, shastic numerics, and mathematical finance.

Table of Contents

Preliminaries.- Part I The Basic Theory of SDEs and BSDEs.- Basics of Shastic Calculus.- Shastic Differential Equations.- Backward Shastic Differential Equations.- Markov BSDEs and PDEs.- Part II Further Theory of BSDEs.- Reflected BSDEs.- BSDEs with Quadratic Growth in Z.- Forward Backward SDEs.- Part III The Fully Nonlinear Theory of BSDEs.- Shastic Calculus Under Weak Formulation.- Nonlinear Expectation.- Path Dependent PDEs.- Second Order BSDEs.. Bibliography.- Index.

Editorial Reviews

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 shastic analysis.” (Martin Ondreját, zbMATH 1390.60004, 2018)

From the Publisher