Risk analysis of the copula dependent aggregate discounted claims with Weibull inter-arrival time

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


Official URL: https://www.ukm.my/jsm/malay_journals/jilid50bil7_...


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.

Item Type:Article
Keywords:FGM copula; Gaver-Stehfest algorithm; Laplace transform; Volterra integral equation; Weibull count model
Journal:Sains Malaysiana
ID Code:17570
Deposited By: ms aida -
Deposited On:11 Nov 2021 01:48
Last Modified:15 Nov 2021 03:54

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