PhD in Applied Mathematics

I am Azar Louzi, a postdoctoral fellow at Fields Institute. I am working with Anastasis Kratsios on foundations of interpretable AI reasoning, with applications to mathematical finance. I am a member of Principles of Intelligence, and am also affiliated with Vector Institute and McMaster University. I am a recipient of the Canada Impact+ Research Training Awards.

I was previously a postdoctoral researcher at LPSM, Sorbonne Université, where I was working with Gilles Pagès. My PhD thesis revolved around Multilevel Approximation Schemes for the Value-at-Risk and Expected Shortfall, and was co-supervised by Stéphane Crépey and Noufel Frikha.

Here is my CV.

Publications

  • Dear GD Where Is the ERM? Estimating the Probability that Gradient Descent Fails on a Universal Attention Head. Anastasis Kratsios, Azar Louzi, Xuwei Yang. Forthcoming.
  • A Weighted Poincaré Inequality for Semi-log-concave Measures. Azar Louzi. Forthcoming.
  • Langevin Dynamics with Lojasiewicz Potentials. Azar Louzi, Gilles Pagès. Forthcoming.
  • Nested Elicitability of the Expected Shortfall. Azar Louzi. Forthcoming.
  • Stochastic Gradient Descent Revisited. Azar Louzi. 2024. arXiv. Hal. Bib.
  • Adaptive Multilevel Stochastic Approximation of the Value-at-Risk. Stéphane Crépey, Noufel Frikha, Azar Louzi, Jonathan Spence. The Annals of Applied Probability 36(5), 2026. DOI. arXiv. Hal. Bib. Code.
  • Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall. Stéphane Crépey, Noufel Frikha, Azar Louzi, Gilles Pagès. Electronic Journal of Probability 29, 1 - 56, 2024. DOI. arXiv. Hal. Bib. Code.
  • A Multilevel Stochastic Approximation Algorithm for Value-at-Risk and Expected Shortfall Estimation. Stéphane Crépey, Noufel Frikha, Azar Louzi. Finance and Stochastics 29, 1015 - 1074, 2025. DOI. arXiv. Hal. Bib. Code.