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arXiv · 2311.15333

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

Stéphane Crépey·Noufel Frikha·Azar Louzi·Gilles Pagès
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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.

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Stéphane Crépey, Noufel Frikha, Azar Louzi, Gilles Pagès. 2023-11-26. Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall. https://doi.org/10.1214/24-ejp1246

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