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A regression-based Monte Carlo method to solve backward stochastic differential equations
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 coefficientsExpand
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Monte-Carlo valuation of American options: facts and new algorithms to improve existing methods
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 basedExpand
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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 differencesExpand
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Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
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 onExpand
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Branching diffusion representation of semilinear PDEs and Monte Carlo approximation
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, introducedExpand
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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
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STochastic OPTimization library in C
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 availableExpand
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A Finite-Dimensional Approximation for Pricing Moving Average Options
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 theExpand
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Machine Learning for Semi Linear PDEs
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 toExpand
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Monte Carlo for high-dimensional degenerated Semi Linear and Full Non Linear PDEs
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 dimensionalityExpand
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