Modeling insurance claims via a mixture exponential model combined with peaks-over-threshold approach

Lee, David; Li, Wai Keung; Wong, Tony Siu Tung

doi:10.1016/j.insmatheco.2012.07.008

Cited by 29 publications

(16 citation statements)

References 14 publications

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“…The semi-parametric bulk model using a mixture of exponentials of Lee, Li, and Wong (2012) is not implemented directly, as it is a special case of the mixture of gammas.…”

Section: Standard Extreme Value Mixture Modelsmentioning

confidence: 99%

evmix: An R package for Extreme Value Mixture Modeling, Threshold Estimation and Boundary Corrected Kernel Density Estimation

Hu¹,

Scarrott²

2018

J. Stat. Soft.

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Abstractevmix is an R package (R Core Team 2017) with two interlinked toolsets: i) for extreme value modeling and ii) kernel density estimation. A key issue in univariate extreme value modeling is the choice of threshold beyond which the asymptotically motivated extreme value models provide a suitable tail approximation. The package implements almost all existing extreme value mixture models, which permit objective threshold estimation and uncertainty quantification. Some traditional diagnostic plots for threshold choice are provided.Kernel density estimation with a range of kernels is provided, including cross-validation maximum likelihood inference for the bandwidth. A key contribution over existing kernel smoothing packages in R is that a wide range of boundary corrected kernel density estimators are implemented, which are designed for populations with bounded support. These non-parametric density estimators are also incorporated into the extreme value mixture model framework to describe the density below the threshold.The quartet of density, distribution, quantile and random number generation functions is provided along with parameter estimation by likelihood inference and standard model fit diagnostics, for both the mixture models and kernel density estimators. The key features of the mixture models and (boundary corrected) kernel density estimators are described and their implementation using the package demonstrated.

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“…The semi-parametric bulk model using a mixture of exponentials of Lee, Li, and Wong (2012) is not implemented directly, as it is a special case of the mixture of gammas.…”

Section: Standard Extreme Value Mixture Modelsmentioning

confidence: 99%

evmix: An R package for Extreme Value Mixture Modeling, Threshold Estimation and Boundary Corrected Kernel Density Estimation

Hu¹,

Scarrott²

2018

J. Stat. Soft.

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“…. ,π n (s)), see for instance Lee et al (2012). In order to estimate the error committed in computing the estimated risk measure ρ s j=1π n (j)µ j instead of the correct one ρ s j=1 π(j)µ j , we employ the theory of large deviations.…”

Section: Ldp For Estimators Of ρ(µ) When µ Is a Mixturementioning

confidence: 99%

“…We refer the interested reader to Lee et al (2012) for a more detailed analysis of the use of exponential mixture models in insurance.…”

Section: Examplesmentioning

confidence: 99%

Large deviations for risk measures in finite mixture models

Bignozzi

Macci

Petrella

2018

Insurance: Mathematics and Economics

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Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is evaluated on the estimated mixture instead of the (unknown) true one, then it is important to investigate the committed error. In this paper we study the asymptotic behaviour of estimated risk measures, as the data sample size tends to infinity, in the fashion of large deviations. We obtain large deviation results by applying the contraction principle, and the rate functions are given by a suitable variational formula; explicit expressions are available for mixtures of two models. Finally, our results are applied to the most common risk measures, namely the quantiles, the Expected Shortfall and the shortfall risk measure.

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“…Nadarajah and Bakar (2014); Bakar et al (2015); Calderín-Ojeda and Kwok (2016) investigate the splicing of the log-normal or Weibull distribution with various tail distributions. Lee et al (2012) consider the splicing of a mixture of two exponentials and the GPD. The use of a mixture model in the first splicing component gives more flexibility in modelling the light and moderate losses.…”

Section: Introductionmentioning

confidence: 99%

Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions

Reynkens

Verbelen

Beirlant

et al. 2017

Insurance: Mathematics and Economics

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In risk analysis, a global fit that appropriately captures the body and the tail of the distribution of losses is essential. Modelling the whole range of the losses using a standard distribution is usually very hard and often impossible due to the specific characteristics of the body and the tail of the loss distribution. A possible solution is to combine two distributions in a splicing model: a light-tailed distribution for the body which covers light and moderate losses, and a heavy-tailed distribution for the tail to capture large losses. We propose a splicing model with a mixed Erlang (ME) distribution for the body and a Pareto distribution for the tail. This combines the flexibility of the ME distribution with the ability of the Pareto distribution to model extreme values. We extend our splicing approach for censored and/or truncated data. Relevant examples of such data can be found in financial risk analysis. We illustrate the flexibility of this splicing model using practical examples from risk measurement.

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Modeling insurance claims via a mixture exponential model combined with peaks-over-threshold approach

Cited by 29 publications

References 14 publications

evmix: An R package for Extreme Value Mixture Modeling, Threshold Estimation and Boundary Corrected Kernel Density Estimation

evmix: An R package for Extreme Value Mixture Modeling, Threshold Estimation and Boundary Corrected Kernel Density Estimation

Large deviations for risk measures in finite mixture models

Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions

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