Stochastic approximation schemes for economic capital and risk margin computations
ESAIM. Proceedings, Tome 65 (2019), pp. 182-218
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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 [17] or by regression à la Broadie, Du, and Moallemi [10]. 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 [17] and [10]. 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 parlance. This is illustrated numerically by a KVA case study implemented on GPUs.
Affiliations des auteurs :
David Barrera 1 ; Stéphane Crépey 2 ; Babacar Diallo 2, 3 ; Gersende Fort 4 ; Emmanuel Gobet 1 ; Uladzislau Stazhynski 1
@article{EP_2019_65_a8,
author = {David Barrera and St\'ephane Cr\'epey and Babacar Diallo and Gersende Fort and Emmanuel Gobet and Uladzislau Stazhynski},
title = {Stochastic approximation schemes for economic capital and risk margin computations},
journal = {ESAIM. Proceedings},
pages = {182--218},
year = {2019},
volume = {65},
doi = {10.1051/proc/201965182},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965182/}
}
TY - JOUR AU - David Barrera AU - Stéphane Crépey AU - Babacar Diallo AU - Gersende Fort AU - Emmanuel Gobet AU - Uladzislau Stazhynski TI - Stochastic approximation schemes for economic capital and risk margin computations JO - ESAIM. Proceedings PY - 2019 SP - 182 EP - 218 VL - 65 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201965182/ DO - 10.1051/proc/201965182 LA - en ID - EP_2019_65_a8 ER -
%0 Journal Article %A David Barrera %A Stéphane Crépey %A Babacar Diallo %A Gersende Fort %A Emmanuel Gobet %A Uladzislau Stazhynski %T Stochastic approximation schemes for economic capital and risk margin computations %J ESAIM. Proceedings %D 2019 %P 182-218 %V 65 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/201965182/ %R 10.1051/proc/201965182 %G en %F EP_2019_65_a8
David Barrera; Stéphane Crépey; Babacar Diallo; Gersende Fort; Emmanuel Gobet; Uladzislau Stazhynski. Stochastic approximation schemes for economic capital and risk margin computations. ESAIM. Proceedings, Tome 65 (2019), pp. 182-218. doi: 10.1051/proc/201965182
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