University of Twente Student Theses

Assessing the Dependency Between Claim Frequency and Claim Severity for a Dutch Home Content Insurance Portfolio : A comparative case study of independent and dependent frequency-severity models

Kingma, Leon (2023) Assessing the Dependency Between Claim Frequency and Claim Severity for a Dutch Home Content Insurance Portfolio : A comparative case study of independent and dependent frequency-severity models.

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Abstract:	This thesis explores the relationship between claim frequency and claim severity in home-content insurance. It investigates whether a model that doesn't assume independence can be preferred. The aim of this thesis is to compare the prediction ability of a frequency-severity model in both the dependent and independent setting. The model where the assumption of dependence between the claim frequency and severity is relaxed can be modelled by including the claim frequency as a covariate in the frequency-severity model. This study will create a framework for insurers in the same or a similar sector to research the relation between the claim frequency and severity. The framework is supported by a literature review that indicated what literature is present and how this study can complement the existing literature in this field. After the literature review, a preliminary analysis regarding the dependency is performed to create first insights into the correlation. In this analysis a negative correlation between the claim frequency and claim severity is discovered. After the literature review and the preliminary analysis, the marginal Generalized Linear Models (GLM) are modelled. With the marginal GLMs for the claim frequency, the claim severity in the independent setting (benchmark) and the claim severity in the dependent setting (adjusted), the total aggregate loss models can be made. These models predict the total aggregate loss on individual policyholder level. The model in the independent setting is a multiplication of the claim frequency GLM and the claim severity GLM. The total aggregate loss model in the dependent setting is similar, but the multiplication is with the adjusted claim severity GLM. Also, a dependency correction term is included. The results of the comparison between these two models regarding the prediction ability indicate a slight preference for the model in the dependent setting. This preference can be explained by the error measures and the distribution of the predicted values compared to the actual values. The model where dependence is allowed has more overlap with the actual values compared to the model where the independence is assumed. Both in-sample and out-ofsample modelling is performed. The validity of the results is therefore increased as the error measures of the in-sample modelling do not indicate a preference over out-ofsample modelling, indicating no overfitting is present. The adjustments in the total aggregate loss model could result in a small economic benefit for Univé Stad en Land as they have the possibility to better predict the total aggregate loss for all policyholders, and thus could be able to determine a more competitive premium.
Item Type:	Essay (Master)
Clients:	Univé Stad en Land, Apeldoorn, Netherlands
Faculty:	BMS: Behavioural, Management and Social Sciences
Subject:	50 technical science in general
Programme:	Industrial Engineering and Management MSc (60029)
Link to this item:	https://purl.utwente.nl/essays/97618
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