article-journal

Asymptotic Error Analysis of the Multilevel Stochastic Approximations of the Value-at-Risk and the Expected Shortfall

This article is a follow up to Crépey, Frikha, and Louzi (2023), where we introduced a nested stochastic approximation algorithm and …

Stéphane Crépey, Noufel Frikha, Azar Louzi, Gilles Pagès

Asymptotic Error Analysis of the Multilevel Stochastic Approximations of the Value-at-Risk and the Expected Shortfall

A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs

Relying on the classical connection between backward stochastic differential equations and nonlinear parabolic partial differential …

Jean-François Chassagneux, Junchao Chen, Noufel Frikha, Chao Zhou

A learning scheme by sparse grids and Picard approximations for semilinear parabolic PDEs

A multilevel stochastic approximation scheme for Value-at-Risk and Expected Shortfall estimation

We propose a multilevel stochastic approximation (MLSA) scheme for the computation of the Value-at-Risk (VaR) and the Expected …

Stéphane Crépey, Noufel Frikha, Azar Louzi

A multilevel stochastic approximation scheme for Value-at-Risk and Expected Shortfall estimation

Well-posedness for some non-linear SDEs and related PDE on the Wasserstein space

In this paper, we investigate the well-posedness of the martingale problem associated to non-linear stochastic differential equations …

Paul-Eric Chaudru de Raynal, Noufel Frikha

Well-posedness for some non-linear SDEs and related PDE on the Wasserstein space

Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift

In this paper, we establish a probabilistic representation as well as some integration by parts formulae for the marginal law at a …

Junchao Chen, Noufel Frikha, Houzhi Li

Probabilistic representation of integration by parts formulae for some stochastic volatility models with unbounded drift

From the backward Kolmogorov PDE on the Wasserstein space to propagation of chaos for McKean-Vlasov SDEs

This article is a continuation of our first work [6]. We here establish some new quantitative estimates for propagation of chaos of …

Paul-Eric Chaudru de Raynal, Noufel Frikha

From the backward Kolmogorov PDE on the Wasserstein space to propagation of chaos for McKean-Vlasov SDEs

Well-posedness and approximation of some one-dimensional Lévy-driven non-linear SDEs

In this article, we are interested in the strong well-posedness together with the numerical approximation of some one-dimensional …

Noufel Frikha, Libo Li

Well-posedness and approximation of some one-dimensional Lévy-driven non-linear SDEs

Well-posedness of some non-linear stable driven SDEs

We prove the well-posedness of some non-linear stochastic differential equations in the sense of McKean-Vlasov driven by non-degenerate …

Noufel Frikha, Valentin Konakov, Stéphane Menozzi

Well-posedness of some non-linear stable driven SDEs

Weak uniqueness and density estimates for SDEs with coefficients depending on some path-functionals

In this article, we develop a methodology to prove weak uniqueness for stochastic differential equations with coefficients depending on …

Noufel Frikha, Libo Li

Integration by parts formula for killed processes: a point of view from approximation theory

In this paper, we establish a probabilistic representation for two integration by parts formulas, one being of Bismut-Elworthy-Li’s …

Noufel Frikha, Arturo Kohatsu-Higa, Libo Li

Integration by parts formula for killed processes: a point of view from approximation theory