Reflected BSDE with a constraint and its application

Reflected BSDE with a constraint and its application

Fri, 18/02/2011
14:15 		Mingyu Xu (Chinese Academy of Sciences, Beijing) Nomura Seminar Add to calendar DH 1st floor SR
Reflected BSDE with a constraint and its application
Non-linear backward stochastic differential equations (BSDEs inshort) 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.