Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time
We model the recursive moments of aggregate discounted claims, assuming the inter-claim arrival time follows a Weibull distribution to accommodate overdispersed and underdispersed data set. We use a copula to represent the dependence structure between the inter-claim arrival time and its subsequent...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Penerbit Universiti Kebangsaan Malaysia
2021
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| Online Access: | http://journalarticle.ukm.my/17570/ http://journalarticle.ukm.my/17570/1/24.pdf |
| _version_ | 1848814346335944704 |
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| author | Siti Norafidah Mohd Ramli, Sharifah Farah Syed Yusoff Alhabshi, Nur Atikah Mohamed Rozali, |
| author_facet | Siti Norafidah Mohd Ramli, Sharifah Farah Syed Yusoff Alhabshi, Nur Atikah Mohamed Rozali, |
| author_sort | Siti Norafidah Mohd Ramli, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | We model the recursive moments of aggregate discounted claims, assuming the inter-claim arrival time follows a Weibull distribution to accommodate overdispersed and underdispersed data set. We use a copula to represent the dependence structure between the inter-claim arrival time and its subsequent claim amount. We then use the Laplace inversion via the Gaver-Stehfest algorithm to solve numerically the first and second moments, which takes the form of a Volterra integral equation (VIE). We compute the average and variance of the aggregate discounted claims under the Farlie-Gumbel-Morgenstern (FGM) copula and conduct a sensitivity analysis under various Weibull inter-claim parameters and claim-size parameters. The comparison between the equidispersed, overdispersed and underdispersed counting processes shows that when claims arrive at times that vary more than is expected, insured lives can expect to pay higher premium, and vice versa for the case of claims arriving at times that vary less than expected. Upon comparing the Weibull risk process with an equivalent Poisson process, we also found that copulas with a wider range of dependency parameter such as the Frank and Heavy Right Tail (HRT), have a greater impact on the value of moments as opposed to modeling under FGM copula with weak dependence structure. |
| first_indexed | 2025-11-15T00:32:37Z |
| format | Article |
| id | oai:generic.eprints.org:17570 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:32:37Z |
| publishDate | 2021 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:175702021-11-15T03:54:08Z http://journalarticle.ukm.my/17570/ Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time Siti Norafidah Mohd Ramli, Sharifah Farah Syed Yusoff Alhabshi, Nur Atikah Mohamed Rozali, We model the recursive moments of aggregate discounted claims, assuming the inter-claim arrival time follows a Weibull distribution to accommodate overdispersed and underdispersed data set. We use a copula to represent the dependence structure between the inter-claim arrival time and its subsequent claim amount. We then use the Laplace inversion via the Gaver-Stehfest algorithm to solve numerically the first and second moments, which takes the form of a Volterra integral equation (VIE). We compute the average and variance of the aggregate discounted claims under the Farlie-Gumbel-Morgenstern (FGM) copula and conduct a sensitivity analysis under various Weibull inter-claim parameters and claim-size parameters. The comparison between the equidispersed, overdispersed and underdispersed counting processes shows that when claims arrive at times that vary more than is expected, insured lives can expect to pay higher premium, and vice versa for the case of claims arriving at times that vary less than expected. Upon comparing the Weibull risk process with an equivalent Poisson process, we also found that copulas with a wider range of dependency parameter such as the Frank and Heavy Right Tail (HRT), have a greater impact on the value of moments as opposed to modeling under FGM copula with weak dependence structure. Penerbit Universiti Kebangsaan Malaysia 2021-07 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/17570/1/24.pdf Siti Norafidah Mohd Ramli, and Sharifah Farah Syed Yusoff Alhabshi, and Nur Atikah Mohamed Rozali, (2021) Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time. Sains Malaysiana, 50 (7). pp. 2109-2121. ISSN 0126-6039 https://www.ukm.my/jsm/malay_journals/jilid50bil7_2021/KandunganJilid50Bil7_2021.html |
| spellingShingle | Siti Norafidah Mohd Ramli, Sharifah Farah Syed Yusoff Alhabshi, Nur Atikah Mohamed Rozali, Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time |
| title | Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time |
| title_full | Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time |
| title_fullStr | Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time |
| title_full_unstemmed | Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time |
| title_short | Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time |
| title_sort | risk analysis of the copula dependent aggregate discounted claims with weibull inter-arrival time |
| url | http://journalarticle.ukm.my/17570/ http://journalarticle.ukm.my/17570/ http://journalarticle.ukm.my/17570/1/24.pdf |