In his forward-looking paper [374] at the conference “Mathematics Towards the Third
Millennium,” our esteemed colleague at Brown University Prof. David Mumford argued that …

A new grid method for computing the Snell envelope of a function of an $\mathbb {R}^ d $-
valued simulatable Markov chain $(X_k) _ {0\lambda\leq k\lambda\leq n} $ is proposed.(This …

In this article, we study the approximation of a probability measure μ on Rd by its empirical
measure ˆμN interpreted as a random quantization. As error criterion we consider an …

This book is an extended written version of the Master 2 course “Probabilités
Numériques”(ie, Numerical Probability or Numerical Methods in Probability) which has been …

We consider the joint SPX & VIX calibration within a general class of Gaussian polynomial
volatility models in which the volatility of the SPX is assumed to be a polynomial function of a …

We present here the quantization method which is well‐adapted for the pricing and hedging
of American options on a basket of assets. Its purpose is to compute a large number of …

We review optimal quantization methods for numerically solving nonlinear problems in
higher dimensions associated with Markov processes. Quantization of a Markov process …

This work presents an empirical analysis of popular scenario generation methods for
stochastic optimization, including quasi-Monte Carlo, moment matching, and methods based …

The aim of this paper is to discuss efficient algorithms for the pricing of American options by
two recently proposed Monte-Carlo type methods, namely the Malliavian calculus and the …

In the paper Bally and Pagès (2000) an algorithm based on an optimal discrete quantization
tree is designed to compute the solution of multi-dimensional obstacle problems for …