Differential equations connecting VaR and CVaR

The Value at Risk (VaR) is a very important risk measure for practitioners, supervisors and researchers. Many practitioners draw on VaR as a critical instrument in Risk Management and other Actuarial/Financial problems, while supervisors and regulators must deal with VaR due to the Basel Accords and...

Descripción completa

Detalles Bibliográficos
Autores: Balbás De La Corte, Alejandro, Balbás, Beatriz, Balbás Aparicio, Raquel
Tipo de recurso: informe técnico
Fecha de publicación:2017
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/22962
Acceso en línea:https://hdl.handle.net/20.500.14352/22962
Access Level:acceso abierto
Palabra clave:C65
G11
G12
G22
VaR and CVaR
Differential equations
VaR representation theorem
Risk optimization and probabilistic constraints
Risk and marginal risk estimation.
Econometría (Economía)
Mercados bursátiles y financieros
Seguros
5302 Econometría
5304.05 Seguros
id ES_0afd6a8a0b739748ec3d79eafdebee00
oai_identifier_str oai:docta.ucm.es:20.500.14352/22962
network_acronym_str ES
network_name_str España
repository_id_str
spelling Differential equations connecting VaR and CVaRBalbás De La Corte, AlejandroBalbás, BeatrizBalbás Aparicio, RaquelC65G11G12G22VaR and CVaRDifferential equationsVaR representation theoremRisk optimization and probabilistic constraintsRisk and marginal risk estimation.Econometría (Economía)Mercados bursátiles y financierosSeguros5302 Econometría5304.05 SegurosThe Value at Risk (VaR) is a very important risk measure for practitioners, supervisors and researchers. Many practitioners draw on VaR as a critical instrument in Risk Management and other Actuarial/Financial problems, while supervisors and regulators must deal with VaR due to the Basel Accords and Solvency II, among other reasons. From a theoretical point of view VaR presents some drawbacks overcome by other risk measures such as the Conditional Value at Risk (CVaR). VaR is neither di¤erentiable nor sub-additive because it is neither continuous nor convex. On the contrary, CVaR satisfies all of these properties, and this simplifies many analytical studies if VaR is replaced by CVaR. In this paper several di¤erential equations connecting both VaR and CVaR will be presented. They will allow us to address several important issues involving VaR with the help of the CVaR properties. This new methodology seems to be very e¢ cient. In particular, a new VaR Representation Theorem may be found, and optimization problems involving VaR or probabilistic constraints always have an equivalent di¤erentiable optimization problem. Applications in VaR, marginal VaR, CVaR and marginal CVaR estimates will be addressed as well. An illustrative actuarial numerical example will be given.Universidad Carlos III de MadridUniversidad Complutense de Madrid20172017-01-0120172017-01-01technical reporthttp://purl.org/coar/resource_type/c_18ghinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/20.500.14352/22962reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución-NoComercial-SinDerivadas 3.0 Españahttps://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/229622026-06-02T12:44:21Z
dc.title.none.fl_str_mv Differential equations connecting VaR and CVaR
title Differential equations connecting VaR and CVaR
spellingShingle Differential equations connecting VaR and CVaR
Balbás De La Corte, Alejandro
C65
G11
G12
G22
VaR and CVaR
Differential equations
VaR representation theorem
Risk optimization and probabilistic constraints
Risk and marginal risk estimation.
Econometría (Economía)
Mercados bursátiles y financieros
Seguros
5302 Econometría
5304.05 Seguros
title_short Differential equations connecting VaR and CVaR
title_full Differential equations connecting VaR and CVaR
title_fullStr Differential equations connecting VaR and CVaR
title_full_unstemmed Differential equations connecting VaR and CVaR
title_sort Differential equations connecting VaR and CVaR
dc.creator.none.fl_str_mv Balbás De La Corte, Alejandro
Balbás, Beatriz
Balbás Aparicio, Raquel
author Balbás De La Corte, Alejandro
author_facet Balbás De La Corte, Alejandro
Balbás, Beatriz
Balbás Aparicio, Raquel
author_role author
author2 Balbás, Beatriz
Balbás Aparicio, Raquel
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv C65
G11
G12
G22
VaR and CVaR
Differential equations
VaR representation theorem
Risk optimization and probabilistic constraints
Risk and marginal risk estimation.
Econometría (Economía)
Mercados bursátiles y financieros
Seguros
5302 Econometría
5304.05 Seguros
topic C65
G11
G12
G22
VaR and CVaR
Differential equations
VaR representation theorem
Risk optimization and probabilistic constraints
Risk and marginal risk estimation.
Econometría (Economía)
Mercados bursátiles y financieros
Seguros
5302 Econometría
5304.05 Seguros
description The Value at Risk (VaR) is a very important risk measure for practitioners, supervisors and researchers. Many practitioners draw on VaR as a critical instrument in Risk Management and other Actuarial/Financial problems, while supervisors and regulators must deal with VaR due to the Basel Accords and Solvency II, among other reasons. From a theoretical point of view VaR presents some drawbacks overcome by other risk measures such as the Conditional Value at Risk (CVaR). VaR is neither di¤erentiable nor sub-additive because it is neither continuous nor convex. On the contrary, CVaR satisfies all of these properties, and this simplifies many analytical studies if VaR is replaced by CVaR. In this paper several di¤erential equations connecting both VaR and CVaR will be presented. They will allow us to address several important issues involving VaR with the help of the CVaR properties. This new methodology seems to be very e¢ cient. In particular, a new VaR Representation Theorem may be found, and optimization problems involving VaR or probabilistic constraints always have an equivalent di¤erentiable optimization problem. Applications in VaR, marginal VaR, CVaR and marginal CVaR estimates will be addressed as well. An illustrative actuarial numerical example will be given.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01
2017
2017-01-01
dc.type.none.fl_str_mv technical report
http://purl.org/coar/resource_type/c_18gh
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/22962
url https://hdl.handle.net/20.500.14352/22962
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-NoComercial-SinDerivadas 3.0 España
https://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-NoComercial-SinDerivadas 3.0 España
https://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad Carlos III de Madrid
publisher.none.fl_str_mv Universidad Carlos III de Madrid
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869403195423326208
score 15,81155

Similares en LA Referencia