Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60G40 Stopping times; optimal stopping problems; gambling theory, See also {62L15, 90D60}
- 90A09 Finance, portfolios, investment
- 65C05 Monte Carlo methods
- 65C20 Models, numerical methods
- 65N50 Mesh generation and refinement

**Résumé:** 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 $\RR^d$-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.

**Mots Clés:** *Numerical Probability ; Optimal Stopping ; Snell envelope ; Quantization of random variables ; Reflected Backward Stochastic Differential Equation ; American option pricing*

**Date:** 2001-03-08

**Prépublication numéro:** *PMA-642*