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This article is a follow up to Cr\'epey, Frikha, and Louzi (2023), where weintroduced a nested stochastic approximation algorithm and its multilevelacceleration for computing the value-at-risk and expected shortfall of a randomfinancial loss. We establish central limit theorems for the renormalized errorsassociated with both algorithms and their averaged variations. Our findings aresubstantiated through numerical examples.

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