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Backward Stochastic Differential Equations

From Linear to Fully Nonlinear Theory

  • Textbook
  • © 2017

Overview

Authors:
  1. Jianfeng Zhang

    1. Department of Mathematics, University of Southern California, Los Angeles, USA

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  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 86)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xv
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  2. Preliminaries

    • Jianfeng Zhang
    Pages 1-18

  3. The Basic Theory of SDEs and BSDEs

    1. Front Matter

      Pages 19-19
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    2. Basics of Stochastic Calculus

      • Jianfeng Zhang
      Pages 21-61

    3. Stochastic Differential Equations

      • Jianfeng Zhang
      Pages 63-78

    4. Backward Stochastic Differential Equations

      • Jianfeng Zhang
      Pages 79-99

    5. Markov BSDEs and PDEs

      • Jianfeng Zhang
      Pages 101-130

  4. Further Theory of BSDEs

    1. Front Matter

      Pages 131-131
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    2. Reflected Backward SDEs

      • Jianfeng Zhang
      Pages 133-160

    3. BSDEs with Quadratic Growth in Z

      • Jianfeng Zhang
      Pages 161-176

    4. Forward-Backward SDEs

      • Jianfeng Zhang
      Pages 177-201

  5. The Fully Nonlinear Theory of BSDEs

    1. Front Matter

      Pages 203-203
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    2. Stochastic Calculus Under Weak Formulation

      • Jianfeng Zhang
      Pages 205-244

    3. Nonlinear Expectation

      • Jianfeng Zhang
      Pages 245-275

    4. Path Dependent PDEs

      • Jianfeng Zhang
      Pages 277-334

    5. Second Order BSDEs

      • Jianfeng Zhang
      Pages 335-364

  6. Back Matter

    Pages 365-386
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Keywords

About this book

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.

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

Authors and Affiliations

  • Department of Mathematics, University of Southern California, Los Angeles, USA

    Jianfeng Zhang

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.

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