Backward Stochastic Differential Equations

From Linear to Fully Nonlinear Theory

Jianfeng Zhang (Autor)

Buch | Hardcover

388 Seiten

2017 | 1st ed. 2017
Springer-Verlag New York Inc.
978-1-4939-7254-8 (ISBN)

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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.

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.

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.

Erscheinungsdatum	19.09.2017
Reihe/Serie	Probability Theory and Stochastic Modelling ; 86
Zusatzinfo	XVI, 388 p.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Wirtschaft ► Allgemeines / Lexika
	Wirtschaft ► Betriebswirtschaft / Management
Schlagworte	backward stochastic differential equations • Economic Theory, Quantitative Economics, Mathematical Methods • Game Theory, Economics, Social and Behavioral Science • mathematical finance • Nonlinear Expectation • Numerical analysis • Parabolic partial differential equations • Partial differential equations • Path Dependent Partial Differential Equations • Probability theory and stochastic processes • Quantitative Finance • Second Order Backward Stochastic Differential Equations • Stochastic Controls • Stochastic differential equations • Viscosity Solutions • Weak formulation
ISBN-10	1-4939-7254-5 / 1493972545
ISBN-13	978-1-4939-7254-8 / 9781493972548
Zustand	Neuware