Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications (Financial Mathematics)

Carmona, René

Society for Industrial & Applied Mathematics,U.S.（2016/11発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 274 p.
• 言語 ENG
• 商品コード 9781611974232
• DDC分類 519.22

Full Description

The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games.

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.

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