It is one of the most challenging problems in applied mathematics to approximatively solve
high-dimensional partial differential equations (PDEs). Recently, several deep learning …

In recent years, tremendous progress has been made on numerical algorithms for solving
partial differential equations (PDEs) in a very high dimension, using ideas from either …

High-dimensional partial differential equations (PDEs) appear in a number of models from
the financial industry, such as in derivative pricing models, credit valuation adjustment …

In this paper, we introduce a numerical method for nonlinear parabolic partial differential
equations (PDEs) that combines operator splitting with deep learning. It divides the PDE …

We develop a multi-stage stochastic programming approach to optimize the bidding strategy
of a virtual power plant (VPP) operating on the Spanish spot market for electricity. The VPP …

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 …

The connection between optimal stopping of random systems and the theory of the Snell
envelop is well understood, and its application to the pricing of American contingent claims …

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 propose a time-space discretization scheme for quasi-linear parabolic PDEs. The
algorithm relies on the theory of fully coupled forward–backward SDEs, which provides an …

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