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

A vital introduction to the stochastic analysis tools which play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. As one of the few books on game theory and the theory of stochastic differential games, this book will be helpful to graduate students and young researchers interested in stochastic differential equations and the probabilistic approach to stochastic control, as well as mean field games and the control of McKeanVlasov dynamics. The theory is illustrated by application to several areas, including application to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading. Based on the author's lecture notes, this is the first title in the SIAM Series on Financial Mathematics. The goal of this textbooks 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. It is designed for 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 the 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