Backward Stochastic Differential Equations

From Linear to Fully Nonlinear Theory
1. Auflage 2017
ISBN: 978-1-4939-7254-8
Verlag: Springer

Buch, Englisch, Band 86, 388 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 7273 g

Reihe: Probability Theory and Stochastic Modelling

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Zhang, Jianfeng

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Wirtschaftstheorie, Wirtschaftsphilosophie
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Preliminaries.- Part I The Basic Theory of SDEs and BSDEs.- Basics of Stochastic Calculus.- Stochastic Differential Equations.- Backward Stochastic 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.- Stochastic Calculus Under Weak Formulation.- Nonlinear Expectation.- Path Dependent PDEs.- Second Order BSDEs. Bibliography.- Index.

Über Autor(innen)

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.