Quantization-based approximation of reflected BSDEs with extended upper bounds for recursive quantization

Understand

We establish upper bounds for the $L^p$-quantization error, p in (1, 2+d), induced by the recursive Markovian quantization of a d-dimensional diffusion discretized via the Euler scheme.

• We introduce a hybrid recursive quantization scheme, easier to implement in the high-dimensional framework, and establish upper bounds to the corresponding $L^p$-quantization error.
• To take advantage of these extensions, we propose a time discretization scheme and a recursive quantization-based discretization scheme associated to a reflected Backward Stochastic Differential Equation and estimate $L^p$-error bounds induced by the space approximation.
• We will explain how to numerically compute the solution of the reflected BSDE relying on the recursive quantization and compare it to other types of quantization.