Generalizirani linearni modeli : završni rad

Vižintin, Marijana (2016) Generalizirani linearni modeli : završni rad. Other, Faculty of Science > Department of Mathematics.

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Abstract

In today's free-market insurer's advantage is charging a premium proportional to the risk that the insurer's takes. Therefore, the production of tariff is one of the most important business processes for insurer. As the market increasingly demands individualization of premiums, insurers are increasingly moving away from simple calculations such as average premiums and defer to increasingly complicated statistical models in an attempt to explain how the claim frequency or claim severity depends on the covariates, i.e. rating factors. Lately most important statistical models used for this purpose are generalized linear models (GLM). They represent a generalization of linear models in two directions. Instead of assuming the normal distribution, GLM uses exponential dispersion models. Furthermore, in GLMs any monotone transformation of the mean is a linear function of covariates. The main advantage of the GLM is a possibility to use a well-developed statistical methods, such as estimating standard errors, constructing confidence intervals, statistical testing and other statistical features. In addition, an important advantage of the GLM is that there is a lot of standard software solutions that are available to everyone, which include everything needed for good data analysis and modeling of GLM's. In the beginning of this thesis, we define the basic terms and explain the reasons for using the multiplicative model, which is a special case of GLM. Then we define the generalized linear models and exponential dispersion models. In particular, distribution of the claim frequency and the claim severity is observed and Tweedie models are defined, the only exponential dispersion models that are scale invariant. After defining of second component of the GLM, the link function, in this paper we give parameter estimation using maximum likelihood method. Furthermore, deviance and AIC criterion are introduced as measure of model fit, and a variety of test statistics with which we can carry out statistical tests and calculate confidence intervals for the parameters. At the very end we give an example of calculating the relativities in the tariff by GLM model for the claim frequency and the claim severity in the programming language R.

Item Type: Thesis (Other)
Supervisor: Basrak, Bojan
Date: 2016
Number of Pages: 47
Subjects: NATURAL SCIENCES > Mathematics
NATURAL SCIENCES > Mathematics > Financial and Business Mathematics
NATURAL SCIENCES > Mathematics > Probability Theory and Statistics
Additional Information: Završni rad na poslijediplomskom specijalističkom studiju aktuarske matematike
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 03 Feb 2016 08:34
Last Modified: 03 Feb 2016 10:20
URI: http://digre.pmf.unizg.hr/id/eprint/4492

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