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Forward-Backward Stochastic Differential Equations and their Applications (Paperback, 1st ed. 1999. Corr. 3rd printing 2007)
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Forward-Backward Stochastic Differential Equations and their Applications (Paperback, 1st ed. 1999. Corr. 3rd printing 2007)
Series: Lecture Notes in Mathematics, 1702
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This book is intended to give an introduction to the theory of
forwa- backward stochastic di erential equations (FBSDEs, for
short) which has received strong attention in recent years because
of its interesting structure and its usefulness in various applied
elds. The motivation for studying FBSDEs comes originally from
stochastic optimal control theory, that is, the adjoint equation in
the Pontryagin-type maximum principle. The earliest version of such
an FBSDE was introduced by Bismut 1] in 1973, with a decoupled
form, namely, a system of a usual (forward)stochastic di erential
equation and a (linear) backwardstochastic dieren tial equation
(BSDE, for short). In 1983, Bensoussan 1] proved the well-posedness
of general linear BSDEs by using martingale representation theorem.
The r st well-posedness result for nonlinear BSDEs was proved in
1990 by Pardoux{Peng 1], while studying the general Pontryagin-type
maximum principle for stochastic optimal controls. A little later,
Peng 4] discovered that the adapted solution of a BSDE could be
used as a pr- abilistic interpretation of the solutions to some
semilinear or quasilinear parabolic partial dieren tial equations
(PDE, for short), in the spirit of the well-known Feynman-Kac
formula. After this, extensive study of BSDEs was initiated, and
potential for its application was found in applied and t- oretical
areas such as stochastic control, mathematical n ance, dieren tial
geometry, to mention a few. The study of (strongly) coupled FBSDEs
started in early 90s. In his Ph.
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