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

Rancy El Nmeir
• Function : Author
Gilles Pagès
• Function : Author
• PersonId : 856726
• IdHAL : gilpag

#### Abstract

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.

#### Domains

Mathematics [math] Probability [math.PR]

### Dates and versions

hal-03890783 , version 1 (08-12-2022)

### Identifiers

• HAL Id : hal-03890783 , version 1
• ARXIV :

### Cite

Rancy El Nmeir, Gilles Pagès. Quantization-based approximation of reflected BSDEs with extended upper bounds for recursive quantization. 2022. ⟨hal-03890783⟩

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