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

Stéphane Crépey (), Noufel Frikha (), Azar Louzi and Gilles Pagès
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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

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Abstract: Crépey, Frikha, and Louzi (2023) 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.

Keywords: value-at-risk; expected shortfall; stochastic approximation; multilevel Monte Carlo; Polyak-Ruppert averaging; central limit theorem (search for similar items in EconPapers)
Date: 2023-11-24
New Economics Papers: this item is included in nep-ecm and nep-rmg
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Published in Electronic Journal of Probability, 2023, 29 (none), ⟨10.1214/24-EJP1246⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-04304985

DOI: 10.1214/24-EJP1246

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