• V. BALLY
• G. PAGÈS

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