Laplace transform on the recursive moments of aggregate discounted claims with Weibull interwaiting time

Siti Norafidah Mohd Ramli, Nur Atikah Mohamed Rozali, Sharifah Farah Syed Yusoff Alhabshi, Ishak Hashim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider aggregate discounted claims of a risk portfolio with Weibull counting process and compute its recursive moments numerically via the Laplace transform. We define the dependence structure between the inter-claim arrival time and its subsequent claims size using the Farlie-Gumbel-Morgenstern (FGM) copula. In our numerical examples, we compare the moments and conduct sensitivity analysis assuming an exponential and a Pareto claims size distribution. We found that despite having similar marginal variances, the risk portfolio with Pareto claims size produces larger moments compared to the corresponding exponential claims size.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018
Subtitle of host publicationInnovative Technologies for Mathematics and Mathematics for Technological Innovation
EditorsYazariah Mohd Yatim, Syakila Ahmad, Mohd Tahir Ismail, Majid Khan Majahar Ali, Rosmanjawati Abdul Rahman, Hajar Sulaiman, Norshafira Ramli, Noor Atinah Ahmad, Farah Aini Abdullah
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735419315
DOIs
Publication statusPublished - 4 Dec 2019
Event1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018 - Penang, Malaysia
Duration: 10 Dec 201812 Dec 2018

Publication series

NameAIP Conference Proceedings
Volume2184
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018
CountryMalaysia
CityPenang
Period10/12/1812/12/18

Fingerprint

moments
sensitivity analysis
arrivals
counting

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Ramli, S. N. M., Rozali, N. A. M., Alhabshi, S. F. S. Y., & Hashim, I. (2019). Laplace transform on the recursive moments of aggregate discounted claims with Weibull interwaiting time. In Y. M. Yatim, S. Ahmad, M. T. Ismail, M. K. M. Ali, R. A. Rahman, H. Sulaiman, N. Ramli, N. A. Ahmad, ... F. A. Abdullah (Eds.), Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation [050017] (AIP Conference Proceedings; Vol. 2184). American Institute of Physics Inc.. https://doi.org/10.1063/1.5136405

Laplace transform on the recursive moments of aggregate discounted claims with Weibull interwaiting time. / Ramli, Siti Norafidah Mohd; Rozali, Nur Atikah Mohamed; Alhabshi, Sharifah Farah Syed Yusoff; Hashim, Ishak.

Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation. ed. / Yazariah Mohd Yatim; Syakila Ahmad; Mohd Tahir Ismail; Majid Khan Majahar Ali; Rosmanjawati Abdul Rahman; Hajar Sulaiman; Norshafira Ramli; Noor Atinah Ahmad; Farah Aini Abdullah. American Institute of Physics Inc., 2019. 050017 (AIP Conference Proceedings; Vol. 2184).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ramli, SNM, Rozali, NAM, Alhabshi, SFSY & Hashim, I 2019, Laplace transform on the recursive moments of aggregate discounted claims with Weibull interwaiting time. in YM Yatim, S Ahmad, MT Ismail, MKM Ali, RA Rahman, H Sulaiman, N Ramli, NA Ahmad & FA Abdullah (eds), Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation., 050017, AIP Conference Proceedings, vol. 2184, American Institute of Physics Inc., 1st International Conference on Mathematical Sciences and Technology 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation, MathTech 2018, Penang, Malaysia, 10/12/18. https://doi.org/10.1063/1.5136405
Ramli SNM, Rozali NAM, Alhabshi SFSY, Hashim I. Laplace transform on the recursive moments of aggregate discounted claims with Weibull interwaiting time. In Yatim YM, Ahmad S, Ismail MT, Ali MKM, Rahman RA, Sulaiman H, Ramli N, Ahmad NA, Abdullah FA, editors, Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation. American Institute of Physics Inc. 2019. 050017. (AIP Conference Proceedings). https://doi.org/10.1063/1.5136405
Ramli, Siti Norafidah Mohd ; Rozali, Nur Atikah Mohamed ; Alhabshi, Sharifah Farah Syed Yusoff ; Hashim, Ishak. / Laplace transform on the recursive moments of aggregate discounted claims with Weibull interwaiting time. Proceedings of the International Conference on Mathematical Sciences and Technology 2018, MathTech 2018: Innovative Technologies for Mathematics and Mathematics for Technological Innovation. editor / Yazariah Mohd Yatim ; Syakila Ahmad ; Mohd Tahir Ismail ; Majid Khan Majahar Ali ; Rosmanjawati Abdul Rahman ; Hajar Sulaiman ; Norshafira Ramli ; Noor Atinah Ahmad ; Farah Aini Abdullah. American Institute of Physics Inc., 2019. (AIP Conference Proceedings).
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