Ruin probability functions and severity of ruin as a statistical decision problem

ABSTRACT: It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the l...

Full description

Bibliographic Details
Authors: Gómez-Déniz, Emilio, Sarabia Alegría, José María|||0000-0002-9619-4721, Calderín-Ojeda, Enrique
Format: article
Publication Date:2019
Country:España
Institution:Universidad de Cantabria (UC)
Repository:UCrea Repositorio Abierto de la Universidad de Cantabria
Language:English
OAI Identifier:oai:repositorio.unican.es:10902/16937
Online Access:http://hdl.handle.net/10902/16937
Access Level:Open access
Keyword:Loss function
Exponential distribution
Pareto distribution
Ruin function
Severity of ruin
Upper bound
id ES_8dda51d4c4a2048d552ab3497af6dfd3
oai_identifier_str oai:repositorio.unican.es:10902/16937
network_acronym_str ES
network_name_str España
repository_id_str
spelling Ruin probability functions and severity of ruin as a statistical decision problemGómez-Déniz, EmilioSarabia Alegría, José María|||0000-0002-9619-4721Calderín-Ojeda, EnriqueLoss functionExponential distributionPareto distributionRuin functionSeverity of ruinUpper boundABSTRACT: It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the loss sustained by a decision-maker who takes as valid a ruin function which is not correct can be considered. By using squared error loss function and appropriate distribution function for these parameters, the issue of estimating the ruin function derives in a mixture procedure. Firstly, a bivariate distribution for mixing jointly the two parameters is considered, and second, different univariate distributions for mixing both parameters separately are examined. Consequently, a catalogue of ruin probability functions and severity of ruin, which are more flexible than the original one, are obtained. The methodology is also extended to the Pareto claim size distribution. Several numerical examples illustrate the performance of these functions.This research was funded by (EGD) [Ministerio de Economía y Competitividad, Spain] grant number [ECO2013–47092]; (EGD)[Ministerio de Economía, Industria y Competitividad. Agencia Estatal de Investigación] grant number [ECO2017–85577–P ]; (JMS) [(Ministerio de Economía, Industria y Competitividad. Agencia Estatal de Investigación] grant number [ECO2016-476203-C2-1-P]; (ECO), research partially carried out while Calderín-Ojeda visited ULPGC as part of his Special Study Program leave, University of Melbourne.Multidisciplinary Digital Publishing Institute (MDPI)Universidad de Cantabria20192019-01-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articlehttp://hdl.handle.net/10902/16937Risks 2019, 7, 68reponame:UCrea Repositorio Abierto de la Universidad de Cantabriainstname:Universidad de Cantabria (UC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial 4.0 Internationalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessoai:repositorio.unican.es:10902/169372026-06-02T12:39:31Z
dc.title.none.fl_str_mv Ruin probability functions and severity of ruin as a statistical decision problem
title Ruin probability functions and severity of ruin as a statistical decision problem
spellingShingle Ruin probability functions and severity of ruin as a statistical decision problem
Gómez-Déniz, Emilio
Loss function
Exponential distribution
Pareto distribution
Ruin function
Severity of ruin
Upper bound
title_short Ruin probability functions and severity of ruin as a statistical decision problem
title_full Ruin probability functions and severity of ruin as a statistical decision problem
title_fullStr Ruin probability functions and severity of ruin as a statistical decision problem
title_full_unstemmed Ruin probability functions and severity of ruin as a statistical decision problem
title_sort Ruin probability functions and severity of ruin as a statistical decision problem
dc.creator.none.fl_str_mv Gómez-Déniz, Emilio
Sarabia Alegría, José María|||0000-0002-9619-4721
Calderín-Ojeda, Enrique
author Gómez-Déniz, Emilio
author_facet Gómez-Déniz, Emilio
Sarabia Alegría, José María|||0000-0002-9619-4721
Calderín-Ojeda, Enrique
author_role author
author2 Sarabia Alegría, José María|||0000-0002-9619-4721
Calderín-Ojeda, Enrique
author2_role author
author
dc.contributor.none.fl_str_mv Universidad de Cantabria
dc.subject.none.fl_str_mv Loss function
Exponential distribution
Pareto distribution
Ruin function
Severity of ruin
Upper bound
topic Loss function
Exponential distribution
Pareto distribution
Ruin function
Severity of ruin
Upper bound
description ABSTRACT: It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the loss sustained by a decision-maker who takes as valid a ruin function which is not correct can be considered. By using squared error loss function and appropriate distribution function for these parameters, the issue of estimating the ruin function derives in a mixture procedure. Firstly, a bivariate distribution for mixing jointly the two parameters is considered, and second, different univariate distributions for mixing both parameters separately are examined. Consequently, a catalogue of ruin probability functions and severity of ruin, which are more flexible than the original one, are obtained. The methodology is also extended to the Pareto claim size distribution. Several numerical examples illustrate the performance of these functions.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10902/16937
url http://hdl.handle.net/10902/16937
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
Attribution-NonCommercial 4.0 International
http://creativecommons.org/licenses/by-nc/4.0/
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
Attribution-NonCommercial 4.0 International
http://creativecommons.org/licenses/by-nc/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute (MDPI)
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute (MDPI)
dc.source.none.fl_str_mv Risks 2019, 7, 68
reponame:UCrea Repositorio Abierto de la Universidad de Cantabria
instname:Universidad de Cantabria (UC)
instname_str Universidad de Cantabria (UC)
reponame_str UCrea Repositorio Abierto de la Universidad de Cantabria
collection UCrea Repositorio Abierto de la Universidad de Cantabria
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869413080505516032
score 15.300724

Similar Items