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

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Listed:
  • St'ephane Cr'epey
  • Noufel Frikha
  • Azar Louzi
  • Gilles Pag`es

Abstract

This article is a follow up to Cr\'epey, 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.

Suggested Citation

  • St'ephane Cr'epey & Noufel Frikha & Azar Louzi & Gilles Pag`es, 2023. "Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall," Papers 2311.15333, arXiv.org.
    • Handle: RePEc:arx:papers:2311.15333
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    References listed on IDEAS

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    1. O. Bardou & N. Frikha & G. Pagès, 2016. "CVaR HEDGING USING QUANTIZATION-BASED STOCHASTIC APPROXIMATION ALGORITHM," Mathematical Finance, Wiley Blackwell, vol. 26(1), pages 184-229, January.
    2. Michael B. Giles & Abdul-Lateef Haji-Ali & Jonathan Spence, 2023. "Efficient Risk Estimation for the Credit Valuation Adjustment," Papers 2301.05886, arXiv.org.
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