Backward Stochastic Differential Equations From Linear to Fully Nonlinear Theory /

• Κύριος συγγραφέας: Zhang, Jianfeng (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York : Imprint: Springer, 2017.
• Σειρά: Probability Theory and Stochastic Modelling, 86
• Θέματα: Mathematics.; Partial differential equations.; Game theory.; Economics, Mathematical.; Numerical analysis.; Probabilities.; Economic theory.; Probability Theory and Stochastic Processes.; Quantitative Finance.; Game Theory, Economics, Social and Behav. Sciences.; Partial Differential Equations.; Numerical Analysis.; Economic Theory/Quantitative Economics/Mathematical Methods.

 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. 

 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.