|
Non-linear
backward stochastic differential equations (BSDEs
in short)
were firstly introduced by Pardoux and Peng (\cite{PP1990}, 1990), who proved the existence and
uniqueness of the adapted
solution, under smooth square integrability
assumptions on the coefficient
and the terminal condition, and when the coefficient $g(t,\omega
,y,z)$ is Lipschitz in $(y,z)$ uniformly in $(t,\omega)$. From then on, the theory
of backward stochastic differential equations (BSDE) has been widely and rapidly
developed. And many problems
in mathematical finance can be treated as BSDEs.
The natural
connection between BSDE and partial differential equations (PDE) of parabolic
and elliptic types is also important applications.
In this talk, we study a new developement
of BSDE, BSDE with contraint and reflecting barrier. The existence and
uniqueness results are presented and we will give some application of this kind of BSDE at
last.
|