Open Access Article SciPap-807
Collective Risk Model in Heterogeneous Portfolios of Policies
by Viera Pacáková 1 iD icon and David Zapletal 2 iD icon

1 Faculty of Economics and Administration, Institute of Mathematics and Quantitative Methods, University of Pardubice, Studenská 84, Pardubice 53210, Czechia

2 Faculty of Economics and Administration, Institute of Mathematics and Quantitative Methods, University of Pardubice, Studenská 84, Pardubice 53210, Czechia

* Authors to whom correspondence should be addressed.

Abstract: 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.

Keywords: Collective Risk Model, Heterogeneous Portfolio Of Policies, Mixture Distributions, Negative Binomial Distribution, Pareto Distribution

JEL classification:  C1 - Econometric and Statistical Methods and Methodology: General,  C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling,  C8 - Data Collection and Data Estimation Methodology • Computer Programs,  G0 - General

SciPap 2016, 24(2), 807

Received: 1 May 2016 / Accepted: 8 September 2016 / Published: 16 September 2016