Theoretical analysis demonstrates solvable doubly reflected backward SDEs under continuous coefficients, indicating robust foundations for bounded stochastic models.
In this work we prove the existence of a solution for a doubly reflected backward SDE with a continuous linearly increasing coefficient in the case where the barriers L and U are such that L < U on [0,T) and there exists a continuous semimartingale between L and U.
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Lepeltier et al. (2004) studied this question.
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