Error analysis of the quantization algorithm for obstacle problems

TitleError analysis of the quantization algorithm for obstacle problems
Publication TypeJournal Article
Year of Publication2003
AuthorsVlad Bally, and Gilles Pagès
JournalStochastic Processes & Their Applications
Start Page1-40
KeywordsAmerican option pricing, Numerical Probability, Optimal Stopping, Quantization of random variables, Reflected Backward Stochastic Differential Equation, Snell envelope

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.