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

Abstract

Crépey, 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.

56 pages, 1 figure, 4 tables

Cited by in corpus (1)

• A Multilevel Stochastic Approximation Algorithm for Value-at-Risk and Expected Shortfall Estimation