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Count copula regression model using generalized beta distribution of the second kind

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Safari-Katesari H., Zaroudi S.
Statistics in Transition new series
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2020
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vol. 21
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issue 2
1-12
EN
Modelling claims severity for obtaining insurance premium is one of the major concerns of the insurance industry. There is a considerable amount of literature on the actuarial application of the copula model to calculate the pure premium. In this paper, we model claims severity for computing the pure premium in the collision market by means of the count copula model. Moreover, we apply a regression model using a generalized beta distribution of the second kind (GB2) to compute the premium for an average claim and the conditional computation for all coverage levels. Like many other researchers, we assume that the number of accidents is independent from the size of claims. For real data application, we use a portfolio of a major automobile insurer in Iran in 2007-2008, with a subsample of 59,547 policies available in their portfolio. We then proceed to compare the estimated premiums with the real premiums. The results demonstrate that there is strong positive dependency between the real premium and the estimated one.
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Analysing the impact of dependency on conditional survival functions using copulas

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Safari-Katesari H., Zaroudi S.
Statistics in Transition new series
|
2021
|
vol. 22
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issue 1
217-226
EN
Nowadays, insurance contract reserves for coupled lives are considered jointly, which has a significant influence on the process of determining actuarial reserves. In this paper, conditional survival distributions of life insurance reserves are computed using copulas. Subsequently, the results are compared with an independence case. These calculations are based on selected Archimedean copulas and apply when the 'death of one individual' condition exists. The estimation outcome indicates that the insurer reserves calculated by means of Archimedean copulas are far more effective than those resulting from an independence assumption. The study demonstrates that copula-based dependency modelling improves the calculations of reserves made for actuarial purposes.
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