English

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

Risk Management 2026-04-14 v5 Probability Computational Finance

Abstract

Cr\'epey, Frikha, and Louzi (2025) introduced a nested stochastic approximation algorithm and its multilevel acceleration to compute the value-at-risk and expected shortfall of a random financial loss. We hereby establish central limit theorems for the renormalized estimation errors associated with both algorithms as well as their averaged versions. Our findings are substantiated through a numerical example.

Keywords

Cite

@article{arxiv.2311.15333,
  title  = {Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall},
  author = {Stéphane Crépey and Noufel Frikha and Azar Louzi and Gilles Pagès},
  journal= {arXiv preprint arXiv:2311.15333},
  year   = {2026}
}

Comments

56 pages, 1 figure, 4 tables