Collective risk model in heterogeneous portfolios of policies
Článekpeer-reviewedpublishedDatum publikování
2016
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Název časopisu
Název svazku
Vydavatel
Univerzita Pardubice
Abstrakt
The total amount of claims in a particular time period, in actuarial literature named as collective risk, is a quantity of fundamental importance to the proper management of an insurance company. The article aimed to present the possibility and procedure to approximate the collective risk model in a heterogeneous portfolio of policies. The key assumption in all models for aggregate claim amount is that the occurrence of a claim and the amount of a claim can be studied separately. We will show that mixture distributions are convenient as the probability models for claim numbers and for claim amounts in heterogeneous portfolios of policies. We have derived that the negative binomial distribution can be used as a model for claim frequency and the Pareto distribution as a loss distribution model when the portfolios of policies are not homogeneous. The concept of mixture distributions is an important one in insurance, since insurance companies generally deal with heterogeneous risks. The motor compulsory third party liability insurance is an important branch of non-life insurance in many countries; therefore application of the theoretical results is performed on data from this field.
Rozsah stran
p. 131-143
ISSN
ISSN 1211-555X (Print)
ISSN 1804-8048 (Online)
ISSN 1804-8048 (Online)
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Zdrojový dokument
Scientific papers of the University of Pardubice. Series D, Faculty of Economics and Administration. 37/2016
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open access
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Klíčová slova
collective risk model, heterogeneous portfolio of policies, mixture distributions, negative binomial distribution, pareto distribution