@article {31,
title = {Error analysis of the quantization algorithm for obstacle problems},
journal = {Stochastic Processes \& Their Applications},
volume = {106(1)},
year = {2003},
chapter = {1-40},
abstract = {In the accompanying paper [2] an algorithm based on a "quantized tree" is designed to compute the solution of multi-dimensional obstacle problems for homogeneous $\mathbb{R}^d$-valued Markov chains. It is based on the quantization of probability distributions which yields a dynamic programming formula on a discrete tree. A typical example of such problems is the pricing of multi-asset American style vanilla options. In the first part of the present paper, the analysis of the $L^p$-error is completed. In the second part, we estimate the error induced by the Monte Carlo estimation of the transition weights involved in the (optimal) quantized tree.},
keywords = {American option pricing, Numerical Probability, Optimal Stopping, Quantization of random variables, Reflected Backward Stochastic Differential Equation, Snell envelope},
author = {Vlad Bally and Gilles Pag{\`e}s}
}