HAL CCSD
Quantization-based approximation of reflected BSDEs with extended upper bounds for recursive quantization
Nmeir, Rancy El
Pagès, Gilles
Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)) ; Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
40 pages, 1 figure, 3 tables
hal-03890783
https://cnrs.hal.science/hal-03890783
https://cnrs.hal.science/hal-03890783
2022
ARXIV: 2105.07684
info:eu-repo/semantics/altIdentifier/arxiv/2105.07684
en
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
info:eu-repo/semantics/preprint
Preprints, Working Papers, ...
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.
2022-12-08