Backward Stochastic Differential Equations: From Linear to Fully Nonlinear Theory

Jianfeng Zhang

Ago 2017 · Probability Theory and Stochastic Modelling Aklat 86 · Springer

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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.

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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.