Switching Games of Backward Stochastic Differential Equations

Details Switching Games of Backward Stochastic Differential Equations Switching Games of Backward Stochastic Differential Equations

2008-06-12

arxiv.org/abs/0806.2058v1

Mathematics

Probability

Scientific paper

In this paper, we study the switching game of one-dimensional backward stochastic differential equations (BSDEs). This gives rise to a new type of multi-dimensional obliquely reflected BSDEs, which is a system of BSDEs reflected on the boundary of a special unbounded convex domain along an oblique direction. The existence of the adapted solution is obtained by the penalization method, the monotone convergence, and the a priori estimations. The uniqueness is obtained by a verification method (the first component of any adapted solution is shown to be the vector value of a switching problem for Reflected BSDEs). Finally, we show the existence of both the value and the saddle point for the switching game. More specifically, we prove that the value process of the switching game is given by the first component of the solution of the multi-dimensional obliquely reflected BSDEs and the saddle point can also be constructed using the latter.

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