Bifurcation of attritional and large losses in an additive IBNR environment

Riegel, Ulrich

doi:10.1080/03461238.2014.991423

Cited by 3 publications

(4 citation statements)

References 6 publications

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“…Example 3.3. Throughout this paper, we will apply the discussed approaches to the numerical example from Riegel (2014Riegel ( , 2016. In contrast to Riegel (2016), we do not interpret the (trended) premiums as model volumes v i , but as volume estimates v i in the extended additive model.…”

Section: Loss Ratio Methodsmentioning

confidence: 96%

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A Generalized Loss Ratio Method Dealing With Uncertain Volume Measures

Riegel¹

2018

ASTIN Bull.

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Unlike chain ladder, the loss ratio method requires volume measures. Typically, these volumes are assumed to be known. In practice, however, accurate volume measures are rarely available. We interpret the available volumes as estimators for the true volume measures and analyze the consequences for the loss ratio method. In particular, we calculate the mean squared error of prediction, including uncertainty of volume measures, and derive approximately optimal weights for the observed incremental loss ratios. We then introduce a generalization of the loss ratio method that is tailored to the situation of uncertain volume measures and calculate the prediction uncertainty of this generalized loss ratio method.

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Section: Loss Ratio Methodsmentioning

confidence: 96%

“…For large coefficients of variation, the lognormal is far more plausible than the normal distribution. Methods for removing large losses are described in Gütschow et al (2017) and Riegel (2014Riegel ( , 2016.…”

Section: Model Assumption 4 the Volume Estimate V N Equals The Modelmentioning

confidence: 99%

A Generalized Loss Ratio Method Dealing With Uncertain Volume Measures

Riegel¹

2018

ASTIN Bull.

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“…Several authors proposed reserving methods which separate large and attritional losses. See Riegel (2014Riegel ( , 2016 and the references therein. In this constext, the actuary is faced with a major technical problem: for older accident years, most large losses have already been identified whereas for more recent accident years, less developments are available and a higher percentage of large losses have not yet exceeded the threshold.…”

Section: Introductionmentioning

confidence: 99%

“…In this constext, the actuary is faced with a major technical problem: for older accident years, most large losses have already been identified whereas for more recent accident years, less developments are available and a higher percentage of large losses have not yet exceeded the threshold. This is why appropriate bifurcation techniques have been proposed by Riegel (2014Riegel ( , 2016 to treat large losses on a consistent basis. To avoid these difficulties, we separate here claims with short and long developments.…”

Section: Introductionmentioning

confidence: 99%

Collective loss reserving with two types of claims in motor third party liability insurance

Denuit

Trufin

2018

Journal of Computational and Applied Mathematics

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This paper adopts the new loss reserving approach proposed by Denuit and Trufin (2016), inspired from the collective model of risk theory. But instead of considering the whole set of claims as a collective, two types of claims are distinguished, those claims with relatively short development patterns and claims requiring longer developments. In each case, the total payment per cell is modelled by means of a Compound Poisson distribution with appropriate assumptions about the severities. A case study based on a motor third party liability insurance portfolio observed over 2004-2014 is used to illustrate the approach proposed in this paper. Comparisons with Chain-Ladder are performed and reveal significant differences in best estimates as well as in Value-at-Risk at high probability levels.

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