Modelling losses and locating the tail with the Pareto Positive Stable distribution

Guillén, Montserrat; Prieto, Faustino; Sarabia, José Marı́a

doi:10.1016/j.insmatheco.2011.07.004

Cited by 29 publications

(12 citation statements)

References 23 publications

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“…The sample consists of n = 518 observations of individual claim costs (in thousands of euros). These data were analyzed in previous studies (20,21) .…”

Section: Data and Resultsmentioning

confidence: 99%

What attitudes to risk underlie distortion risk measure choices?

Belles-Sampera

Guillén

Santolino

2016

Insurance: Mathematics and Economics

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Understanding the attitude to risk implicit within a risk measure sheds some light on the way in which decision makers perceive losses. In this paper, a two-stage strategy is developed to characterize the underlying risk attitude involved in a risk evaluation, when executed by the family of distortion risk measures. First, we show that aggregation indicators defined for discrete Choquet integrals provide information about the implicit global risk attitude of the agent. Second, an analysis of the distortion function offers a local description of the agent's stance on risk in relation to the occurrence of accumulated losses. Here, the concepts of absolute risk attitude and local risk attitude arise naturally. An example is provided to illustrate the usefulness of this strategy for characterizing risk attitudes in an insurance company.

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“…The sample consists of n = 518 observations of individual claim costs (in thousands of euros). These data were analyzed in previous studies (20,21) .…”

Section: Data and Resultsmentioning

confidence: 99%

What attitudes to risk underlie distortion risk measure choices?

Belles-Sampera

Guillén

Santolino

2016

Insurance: Mathematics and Economics

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“…The sample consists of n = 518 observations of the cost of individual claims in thousands of euros. These data were previously analyzed in Bolancé et al (2008) and Guillén et al (2011).…”

Section: Illustration Of Risk Measurement Using Gluevarmentioning

confidence: 99%

The use of flexible quantile-based measures in risk assessment

Belles-Sampera

Guillén

Santolino

2015

Communications in Statistics - Theory and Methods

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A new family of distortion risk measures -GlueVaR-is proposed in BellesSampera et al. (2014) to procure a risk assessment lying between those provided by common quantile-based risk measures. GlueVaR risk measures may be expressed as a combination of these standard risk measures. We show here that this relationship may be used to obtain approximations of GlueVaR measures for general skewed distribution functions using the Cornish-Fisher expansion. A subfamily of GlueVaR measures satisfies the tail-subadditivity property. An example of risk measurement based on real insurance claim data is presented, where implications of tail-subadditivity in the aggregation of risks are illustrated.

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“…These data contain n = 519 observations of the cost of individual claims in thousands of euros, and were analyzed in Bolancé et al (8) and Guillén et al (37) . The risk measures for these data are displayed in Table 3.…”

Section: Illustrationmentioning

confidence: 99%

Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures

2013

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We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed‐form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between GlueVaR, value‐at‐risk, and tail value‐at‐risk is explained. Tail subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in nonfinancial problems such as health, safety, environmental, or catastrophic risk management.

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Modelling losses and locating the tail with the Pareto Positive Stable distribution

Cited by 29 publications

References 23 publications

What attitudes to risk underlie distortion risk measure choices?

What attitudes to risk underlie distortion risk measure choices?

The use of flexible quantile-based measures in risk assessment

Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures

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