Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications (SIAM Series on Financial Mathematics, Series Number 1)

This is the first title in SIAM's Financial Mathematics book series and is based on the author s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean-Vlasov dynamics.

The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.

Audience: This book is written for young researchers and newcomers to stochastic control and stochastic differential games.

Contents: Preface; List of Notation; Part I: Stochastic Calculus; Chapter 1: Stochastic Differential Equations; Chapter 2: Backward Stochastic Differential Equations; Part II: Stochastic Control; Chapter 3: Continuous Time Stochastic Optimization and Control; Chapter 4: Probabilistic Approaches to Stochastic Control; Part III: Stochastic Differential Games; Chapter 5: Stochastic Differential Games; Chapter 6: Mean Field Games; Bibliography; Author Index; Subject Index