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This paper is concerned with the switching game of a one-dimensional backward stochastic differential equation (BSDE). The associated Bellman-Isaacs equation is a system of matrix-valued BSDEs living in a special unbounded convex domain with reflection on the boundary along an oblique direction. In this paper, we show the existence of an adapted solution to this system of BSDEs with oblique reflection by the penalization method, the monotone convergence, and the a priori estimates.
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also
The BMO martingale theory is extensively used to study nonlinear multi-dimensional stochastic equations (SEs) in $cR^p$ ($pin [1, infty)$) and backward stochastic differential equations (BSDEs) in $cR^ptimes cH^p$ ($pin (1, infty)$) and in $cR^inftyt
This paper introduces the notion of a filtration-consistent dynamic operator with a floor, by suitably formulating four axioms. It is shown that under some suitable conditions, a filtration-consistent dynamic operator with a continuous upper-bounded
In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, cor
In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with L{e}vy process. We obtain