Abstract: We discuss the deterministic limit for a class of convex backward differential equations (BSDE) as the volatility of the driving Brownian motion goes to zero. To a certain degree, this provides a generalization of the classical Schilder Theorem in large deviations theory, where the role of the cumulant generating function is replaced by a more general risk measure. We also discuss how Gaussian fluctuations may also appear in this limit result, after identifying the correct scaling. Time permitting, we finalize with a discussion on the analogue of Sanov's theorem in the setting of BSDE. Based on joint work with D. Lacker and L. Tangpi, as well as communications with M. Shkolnikov.
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