Skewed bivariate models and nonparametric estimation for the CTE risk measure

Bolancé, Catalina; Guillén, Montserrat; Pelican, Elena; Vernic, Raluca

doi:10.1016/j.insmatheco.2008.07.005

Cited by 55 publications

(48 citation statements)

References 33 publications

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“…En conjunto, los indicadores usados determinaron que las distribuciones skew-normal y skew-t son las que mejor describen al logaritmo del coste de los siniestros, tanto en las coberturas de seguros de Invalidez como de Sobrevivencia. Para los dos grupos de datos estudiados, la distribución skew-normal se ajusta mejor en comparación con la distribución skew-t. Los resultados confirman las ideas planteadas por Bolance et al (2008) y Eling (2011 en sus publicaciones, que plantean la utilidad de las distribuciones estudiadas en el área de seguros.…”

Section: Conclusionesunclassified

Análisis del coste de los siniestros en una compañía de seguros utilizando las distribuciones asimétricas skew-normal y skew-t

Vásquez

Quevedo²

2017

An. cient. U.N.A.

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Análisis del coste de los siniestros en una compañía de seguros utilizando las distribuciones asimétricas skew-normal y skew-tAnalysis of the cost of claims at an insurance company using skew-normal and skew-t asymmetric distributions 1 *Carlos López de Castilla Vásquez y 2 Diego Alonso Mendoza Quevedo Resumen La presente investigación tiene por objetivo principal determinar si las distribuciones asimétricas skew-normal y skew-t son buenos modelos para describir datos relativos al coste de los siniestros. Para lo cual se analizaron dos conjuntos de datos de una compañía de seguros, ajustando las distribuciones en estudio y las tradicionales a estos datos. Luego se compararon las distribuciones empleando el Criterio de Información de Akaike (AIC) y del Logaritmo de la función de Verosimilitud, complementados con la prueba de bondad de ajuste Kolmogorov-Smirnov, obteniendo resultados positivos. Además, se calcularon medidas de riesgo como el Valor en Riesgo (VaR) y el Valor en Riesgo Condicional (TVaR), que brindaron mayor solidez a los resultados previos: los costes de los siniestros en los seguros se ajustan bien a las distribuciones asimétricas skew-normal y skew-t. Palabras clave en español: Distribucion asimetrica, skew-normal, skew-t, VaR, TVaR AbstractThe main purpose of this research is to determine if the skew-normal and skew-t asymmetric distributions are good models to describe data related to the claim cost. Therefore, two data sets of an insurance company were analyzed, fitting the studied and the traditional distributions to said data. Then distributions were compared using the Akaike Information Criterion (AIC) and the Likelihood function Logarithm, supplemented by the Kolmogorov-Smirnov goodness-of-fit test, obtaining positive results. In addition, risk measurements were calculated, such as the Value-at-Risk (VaR) and the Tail Value-at-Risk (TVaR) which provided greater strength to the previous results: the claim costs in the insurances fit well to the skew-normal and skew-t asymmetric distributions.

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Section: Conclusionesunclassified

Análisis del coste de los siniestros en una compañía de seguros utilizando las distribuciones asimétricas skew-normal y skew-t

Vásquez

Quevedo²

2017

An. cient. U.N.A.

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“…Analyzing the distribution of S is essential in finance and insurance for quantifying the risk of loss. In this regard, there are studies that have analyzed the stochastic behaviour of the sum of dependent risks and the way in which the dependency between these marginal risks may affect the total risk of loss (see, Denuit et al, 1999;Kaas et al, 2000;Cossette et al, 2002;Bolancé et al, 2008b). The aim of this paper is to analyze the test proposed by Kojadinovic et al (2011) that allows to test whether or not our data have been generated by an extreme value copula.…”

Section: Introductionmentioning

confidence: 99%

Testing Extreme Value Copulas to Estimate the Quantile

2013

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We generalize the test proposed by Kojadinovic, Segers and Yan which is used for testing whether the data belongs to the family of extreme value copulas. We prove that the generalized test can be applied whatever the alternative hypothesis. We also study the effect of using different extreme value copulas in the context of risk estimation. To measure the risk we use a quantile. Our results have been motivated by a bivariate sample of losses from a real database of auto insurance claims.MSC: MSC62-07 MSC62F05.

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“…Despite their extensive application, the theoretical properties of these distributions are not always empirically matched by observed stylized facts of insurance data. Recently Bolance et al (2008) provides strong empirical evidence in favor of the use of the Skew Normal, and log-Skew Normal distributions to model bivariate claims data from the Spanish motor insurance industry, while Ahn et al (2012) use the log Phase-type distribution as a parametric alternative in fitting heavy tailed data. Eling (2012) shows that the Skew Normal and the Skew-Student t distributions are reasonably competitive compared to other models when describing insurance data.…”

Section: Introductionmentioning

confidence: 99%

Skew mixture models for loss distributions: A Bayesian approach

Bernardi

Maruotti

Petrella

2012

Insurance: Mathematics and Economics

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The derivation of loss distribution from insurance data is a very interesting research topic but at the same time not an easy task. To find an analytic solution to the loss distribution may be mislading although this approach is frequently adopted in the actuarial literature. Moreover, it is well recognized that the loss distribution is strongly skewed with heavy tails and present small, medium and large size claims which hardly can be fitted by a single analytic and parametric distribution. Here we propose a finite mixture of Skew Normal distributions that provides a better characterization of insurance data. We adopt a Bayesian approach to estimate the model, providing the likelihood and the priors for the all unknow parameters; we implement an adaptive Markov Chain Monte Carlo algorithm to approximate the posterior distribution. We apply our approach to a well known Danish fire loss data and relevant risk measures, as Value-at-Risk and Expected Shortfall probability, are evaluated as well.

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Skewed bivariate models and nonparametric estimation for the CTE risk measure

Cited by 55 publications

References 33 publications

Análisis del coste de los siniestros en una compañía de seguros utilizando las distribuciones asimétricas skew-normal y skew-t

Análisis del coste de los siniestros en una compañía de seguros utilizando las distribuciones asimétricas skew-normal y skew-t

Testing Extreme Value Copulas to Estimate the Quantile

Skew mixture models for loss distributions: A Bayesian approach

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