Autumn 2001, MWF 10:30-11:20
Forward-backward stochastic differential equations (FBSDE in abbreviation) is a system of a usual (forward) stochastic differential equation and a backward stochastic differential equation (BSDE in short). The study of FBSDE originated from stochastic optimal control theory. The earlier version of such FBSDE was introduced in 1973 by Bismut. The systematic study of such equations started in 1990 and its connection with nonlinear differential equations was found. The FBSDE has been applied areas such as stochastic control, mathematical finance and differential equations.
In this course, I plan to cover some basic theory of FBSDE and its applications, starting with some motivating examples. Topics will include well-posedness of BSDE, solvability of FBSDE, comparison theorems for BSDE and FBSDE, solving FBSDE using Four Step Scheme and Method of Continuation. If time permits, we may also discuss applications of FBSDE and
the numerical methods for FBSDE.
Reference Book
J. Ma and J. Yong, {\it Forward-Backward Stochastic Differential Equations and their Applications, Springer-Verlag, Berlin Heidelberg, 1999.
Prerequisites:
Knowledge about martingales and Brownian motion is needed to take this course. Math/Stat 521-2-3 or equivalent is desirable.