Backward Stochastic Differential Equations

From Linear to Fully Nonlinear Theory

  • Jianfeng┬áZhang

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

Table of contents

  1. Front Matter
    Pages i-xv
  2. Jianfeng Zhang
    Pages 1-18
  3. The Basic Theory of SDEs and BSDEs

    1. Front Matter
      Pages 19-19
    2. Jianfeng Zhang
      Pages 21-61
    3. Jianfeng Zhang
      Pages 63-78
    4. Jianfeng Zhang
      Pages 79-99
    5. Jianfeng Zhang
      Pages 101-130
  4. Further Theory of BSDEs

    1. Front Matter
      Pages 131-131
    2. Jianfeng Zhang
      Pages 133-160
    3. Jianfeng Zhang
      Pages 161-176
    4. Jianfeng Zhang
      Pages 177-201
  5. The Fully Nonlinear Theory of BSDEs

    1. Front Matter
      Pages 203-203
    2. Jianfeng Zhang
      Pages 205-244
    3. Jianfeng Zhang
      Pages 245-275
    4. Jianfeng Zhang
      Pages 277-334
    5. Jianfeng Zhang
      Pages 335-364
  6. Back Matter
    Pages 365-386

About this book

Introduction

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.

Keywords

Stochastic Differential Equations Backward Stochastic Differential Equations Second Order Backward Stochastic Differential Equations Path Dependent Partial Differential Equations Parabolic Partial Differential Equations Nonlinear Expectation Stochastic Controls Mathematical Finance Viscosity Solutions Weak Formulation Probability Theory and Stochastic Processes Quantitative Finance Game Theory, Economics, Social and Behavioral Science Partial Differential Equations Numerical Analysis Economic Theory, Quantitative Economics, Mathematical Methods

Authors and affiliations

  • Jianfeng┬áZhang
    • 1
  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-7256-2
  • Copyright Information Springer Science+Business Media LLC 2017
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-7254-8
  • Online ISBN 978-1-4939-7256-2
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • About this book