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- Publications
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A regression-based Monte Carlo method to solve backward stochastic differential equations

- E. Gobet, Jean-Philippe Lemor, X. Warin
- Mathematics
- 1 August 2005

We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients… Expand

Monte-Carlo valuation of American options: facts and new algorithms to improve existing methods

- B. Bouchard, X. Warin
- Mathematics
- 2 May 2012

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 regression based… Expand

A Probabilistic Numerical Method for Fully Nonlinear Parabolic PDEs

We consider the probabilistic numerical scheme for fully nonlinear PDEs suggested in \cite{cstv}, and show that it can be introduced naturally as a combination of Monte Carlo and finite differences… Expand

Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations

- Jean-Philippe Lemor, E. Gobet, X. Warin
- Mathematics
- 1 October 2006

This study focuses on the numerical resolution of backward stochastic differential equations with data dependent on a jump-diffusion process. We propose and analyse a numerical scheme based on… Expand

Branching diffusion representation of semilinear PDEs and Monte Carlo approximation

- P. Henry-Labordère, N. Oudjane, Xiaolu Tan, N. Touzi, X. Warin
- Mathematics
- 5 March 2016

We provide a representation result of parabolic semi-linear PD-Es, with polynomial nonlinearity, by branching diffusion processes. We extend the classical representation for KPP equations, introduced… Expand

Some machine learning schemes for high-dimensional nonlinear PDEs

We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE)… Expand

STochastic OPTimization library in C

- Hugo Gevret, J. Lelong, X. Warin
- Computer Science
- 7 September 2016

The STochastic OPTimization library (StOpt) aims at providing tools in C++ for solving some
stochastic optimization problems encountered in finance or in the industry.
A python binding is available… Expand

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A Finite-Dimensional Approximation for Pricing Moving Average Options

- Marie Bernhart, Peter Tankov, Xavier Warin
- Mathematics, Computer Science
- SIAM J. Financial Math.
- 15 November 2010

We propose a method for pricing American options whose payoff depends on the moving average of the underlying asset price. The method uses a finite-dimensional approximation of the… Expand

Machine Learning for Semi Linear PDEs

- Quentin Chan-Wai-Nam, Joseph Mikael, X. Warin
- Mathematics, Computer Science
- J. Sci. Comput.
- 20 September 2018

Recent machine learning algorithms dedicated to solving semi-linear PDEs are improved by using different neural network architectures and different parameterizations. These algorithms are compared to… Expand

Monte Carlo for high-dimensional degenerated Semi Linear and Full Non Linear PDEs

- X. Warin
- Mathematics
- 14 May 2018

We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion. Being a pure Monte Carlo method it does not suffer from the so called curse of dimensionality… Expand