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

Author

Listed:
  • Stéphane Crépey

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

  • Noufel Frikha

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Azar Louzi

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

  • Gilles Pagès

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

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.

Suggested Citation

  • Stéphane Crépey & Noufel Frikha & Azar Louzi & Gilles Pagès, 2023. "Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall," Working Papers hal-04304985, HAL.
    • Handle: RePEc:hal:wpaper:hal-04304985
    Note: View the original document on HAL open archive server: https://hal.science/hal-04304985
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