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

Abstract

This article is a follow up to Crépey, Frikha, and Louzi (2023), where we introduced a nested stochastic approximation algorithm and its multilevel acceleration for computing the value-at-risk and expected shortfall of a random financial loss. We establish central limit theorems for the renormalized errors associated with both algorithms and their averaged variations. Our findings are substantiated through numerical examples.