Stochastic Approximation Schemes for Economic Capital and Risk Margin Computations

David Barrera, Stéphane Crépey (), Babacar Diallo (), Gersende Fort (), Emmanuel Gobet () and Uladzislau Stazhynski
Additional contact information
David Barrera: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Stéphane Crépey: LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique
Babacar Diallo: LMEE - Laboratoire de Mécanique et d'Energétique d'Evry - UEVE - Université d'Évry-Val-d'Essonne
Gersende Fort: IMT - Institut de Mathématiques de Toulouse UMR5219 - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INSA Toulouse - Institut National des Sciences Appliquées - Toulouse - INSA - Institut National des Sciences Appliquées - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique
Emmanuel Gobet: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Uladzislau Stazhynski: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: We consider the problem of the numerical computation of its economic capital by an insurance or a bank, in the form of a value-at-risk or expected shortfall of its loss over a given time horizon. This loss includes the appreciation of the mark-to-model of the liabilities of the firm, which we account for by nested Monte Carlo à la Gordy and Juneja (2010) or by regression à la Broadie, Du, and Moallemi (2015). Using a stochastic approximation point of view on value-at-risk and expected shortfall, we establish the convergence of the resulting economic capital simulation schemes, under mild assumptions that only bear on the theoretical limiting problem at hand, as opposed to assumptions on the approximating problems in Gordy-Juneja (2010) and Broadie-Du-Moallemi (2015). Our economic capital estimates can then be made conditional in a Markov framework and integrated in an outer Monte Carlo simulation to yield the risk margin of the firm, corresponding to a market value margin (MVM) in insurance or to a capital valuation adjustment (KVA) in banking par- lance. This is illustrated numerically by a KVA case study implemented on GPUs.

Date: 2019
New Economics Papers: this item is included in nep-cmp, nep-ias and nep-rmg
Note: View the original document on HAL open archive server: https://hal.science/hal-01710394v1
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in ESAIM: Proceedings and Surveys, 2019, 65, pp.182-218. ⟨10.1051/proc/201965182⟩

Downloads: (external link)
https://hal.science/hal-01710394v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01710394

DOI: 10.1051/proc/201965182

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().