Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year
[EN] In the current context of Solvency II, insurance companies are required to implement demanding business risk management systems. An important aspect of this risk management is the problem of technical provisions in non-life insurance and, as such, it is in the interest of insurers to calculate...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/21773 |
| Acceso en línea: | http://hdl.handle.net/10810/21773 |
| Access Level: | acceso abierto |
| Palabra clave: | technical provisions generalized linear model calendar year solvency II provisiones técnicas modelo lineal generalizado año de calendario solvencia II C13 C15 |
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oai:addi.ehu.eus:10810/21773 |
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ES |
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España |
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| dc.title.none.fl_str_mv |
Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year Cálculo de provisiones para prestaciones pendientes de declaración con modelos lineales generalizados: formulación del error de predicción por año de calendario |
| title |
Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year |
| spellingShingle |
Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year Boj del Val, Eva technical provisions generalized linear model calendar year solvency II provisiones técnicas modelo lineal generalizado año de calendario solvencia II C13 C15 C13 C15 |
| title_short |
Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year |
| title_full |
Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year |
| title_fullStr |
Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year |
| title_full_unstemmed |
Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year |
| title_sort |
Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year |
| dc.creator.none.fl_str_mv |
Boj del Val, Eva Costa Cor, Teresa |
| author |
Boj del Val, Eva |
| author_facet |
Boj del Val, Eva Costa Cor, Teresa |
| author_role |
author |
| author2 |
Costa Cor, Teresa |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
technical provisions generalized linear model calendar year solvency II provisiones técnicas modelo lineal generalizado año de calendario solvencia II C13 C15 C13 C15 |
| topic |
technical provisions generalized linear model calendar year solvency II provisiones técnicas modelo lineal generalizado año de calendario solvencia II C13 C15 C13 C15 |
| description |
[EN] In the current context of Solvency II, insurance companies are required to implement demanding business risk management systems. An important aspect of this risk management is the problem of technical provisions in non-life insurance and, as such, it is in the interest of insurers to calculate the prediction error that has occurred when using methodology to estimate a company’s future payments. Furthermore, the predictive distribution of the fitted values, which is descriptive of the risk, allows us to estimate, for example, its Value at Risk at a given confidence level. In this paper we focus on the application of generalized linear models to the amounts of claim losses of a run-off triangle. In order to achieve error distribution, a parameter dependent parametric family is assumed, along with the logarithmic link function. The parametric family has as particular cases the Poisson, the Gamma and the Inverse Gaussian distributions. The particular case which assumes an (over-dispersed) Poisson distribution with the logarithmic link is widely known because it offers the same provision estimation as the deterministic Chain-Ladder method. In this study we develop formulas of the prediction error of future payments by calendar years for the general parametric family. This allows us to perform calculations that consider a financial environment, whether employing analytical formulation or bootstrap estimation. In practice, the presented formulations allow a determination to be made of the present value of the incurred but not reported claim of future payments including a risk margin with statistical significance. |
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2017 |
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2017 2017 2017 |
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info:eu-repo/semantics/article |
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article |
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http://hdl.handle.net/10810/21773 |
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http://hdl.handle.net/10810/21773 |
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Inglés |
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Inglés |
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info:eu-repo/grantAgreement/MEC/MTM2010-17323/ http://www.ehu.eus/cuadernosdegestion/revista/en/published-issues/articulo?year=2017&vol=17&num=2&o=7 |
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info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Atribución-NoComercial-SinDerivadas 3.0 España |
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openAccess |
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http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Atribución-NoComercial-SinDerivadas 3.0 España |
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application/pdf |
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Instituto de Economía Aplicada a la Empresa (Universidad del País Vasco UPV/EHU) |
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Instituto de Economía Aplicada a la Empresa (Universidad del País Vasco UPV/EHU) |
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reponame:Addi. Archivo Digital para la Docencia y la Investigación instname:Universidad del País Vasco |
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Universidad del País Vasco |
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Addi. Archivo Digital para la Docencia y la Investigación |
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Addi. Archivo Digital para la Docencia y la Investigación |
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1869405641973432320 |
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Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar yearCálculo de provisiones para prestaciones pendientes de declaración con modelos lineales generalizados: formulación del error de predicción por año de calendarioBoj del Val, EvaCosta Cor, Teresatechnical provisionsgeneralized linear modelcalendar yearsolvency IIprovisiones técnicasmodelo lineal generalizadoaño de calendariosolvencia IIC13C15C13C15[EN] In the current context of Solvency II, insurance companies are required to implement demanding business risk management systems. An important aspect of this risk management is the problem of technical provisions in non-life insurance and, as such, it is in the interest of insurers to calculate the prediction error that has occurred when using methodology to estimate a company’s future payments. Furthermore, the predictive distribution of the fitted values, which is descriptive of the risk, allows us to estimate, for example, its Value at Risk at a given confidence level. In this paper we focus on the application of generalized linear models to the amounts of claim losses of a run-off triangle. In order to achieve error distribution, a parameter dependent parametric family is assumed, along with the logarithmic link function. The parametric family has as particular cases the Poisson, the Gamma and the Inverse Gaussian distributions. The particular case which assumes an (over-dispersed) Poisson distribution with the logarithmic link is widely known because it offers the same provision estimation as the deterministic Chain-Ladder method. In this study we develop formulas of the prediction error of future payments by calendar years for the general parametric family. This allows us to perform calculations that consider a financial environment, whether employing analytical formulation or bootstrap estimation. In practice, the presented formulations allow a determination to be made of the present value of the incurred but not reported claim of future payments including a risk margin with statistical significance.[ES] El actual contexto de Solvencia II requiere una exigente gestión empresarial del riesgo de las Entidades Aseguradoras. En el problema de cálculo de provisiones técnicas en seguros de no-vida es de interés calcular el error de predicción cometido con la metodología utilizada para la estimación de los pagos futuros de la Entidad. Además, la distribución predictiva de las estimaciones, que es descriptiva respecto del riesgo, permite obtener, por ejemplo, su valor en riesgo a un nivel de confianza fijado. En este trabajo nos centramos en la aplicación de los modelos lineales generalizados a las cuantías de siniestros de un triángulo de desarrollo. Asumimos para la distribución del error una familia paramétrica dependiente de un parámetro, junto con la función de enlace logarítmica. La familia paramétrica tiene como casos particulares las distribuciones de Poisson, Gamma e Inversa Gaussiana. Es conocido el caso particular en que se asume una distribución de Poisson (sobredispersa) junto con el link logarítmico, que ofrece la misma estimación de provisiones que el método determinista Chain-Ladder. En este estudio desarrollamos las fórmulas del error de predicción de los pagos futuros por años de calendario para la familia paramétrica general, que nos permiten realizar cálculos teniendo en cuenta un ambiente financiero, tanto para el caso de utilizar formulación analítica como para el caso de realizar estimación bootstrap. En la práctica, las formulaciones presentadas nos ponen en disposición de poder calcular el valor actual de los pagos futuros para siniestros pendientes incluyendo márgenes de riesgo con significado estadístico.Authors have been supported by the Spanish Ministerio de Educación y Ciencia under grant MTM2010-17323 and by the Generalitat de Catalunya, AGAUR under grant 2014SGR152.Instituto de Economía Aplicada a la Empresa (Universidad del País Vasco UPV/EHU)201720172017info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/21773reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoInglésinfo:eu-repo/grantAgreement/MEC/MTM2010-17323/http://www.ehu.eus/cuadernosdegestion/revista/en/published-issues/articulo?year=2017&vol=17&num=2&o=7info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/3.0/es/Atribución-NoComercial-SinDerivadas 3.0 Españaoai:addi.ehu.eus:10810/217732026-06-18T09:23:17Z |
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15,300724 |