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Existence and Uniqueness for Backward Stochastic Differential Equation to Stopping Time
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Author: Junjie Bai, Haiyue Jin, Yicheng Hong, Chol Gyu Pak, Mun Chol Kim
Abstract: In this paper, we prove the existence and uniqueness for Backward Stochastic Differential Equations with stopping time as time horizon under the hypothesis that the generator is bounded. We first prove for the stopping time with finite values and for the general stopping time we prove the result taking limit. We suggest a new approach to generalize the results for the case of constant time horizon to the case of stopping time horizon.
Keywords: BSDE (Backward Stochastic Differential Equation), Random Time Horizon, Stopping Time
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