Laplace transform on the recursive moments of copula-dependent aggregate discounted claims

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

doi:10.1063/1.5041641

Laplace transform on the recursive moments of copula-dependent aggregate discounted claims

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

Universiti Kebangsaan Malaysia

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

We consider the recursive moments of aggregate discounted claims, where the dependence between the inter-claim time and the subsequent claim size is captured by a copula distribution. The equations of the recursive moments, which take the form of the Volterra integral equation (VIE), are then solved using the Laplace transform. We then compute its mean and variance, and compare with the results obtained in previous literature.

Original language	English
Title of host publication	Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017
Subtitle of host publication	Mathematical Sciences as the Core of Intellectual Excellence
Editors	Hamidah Maidinsah, Sarifah Radiah Sharif, Wan Eny Zarina Wan Abdul Rahman, Ajab Bai Akbarally, Mesliza Mohamed, Daud Mohamad, Maheran Mohd Jaffar
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735416819
DOIs	https://doi.org/10.1063/1.5041641
State	Published - 28 Jun 2018
Externally published	Yes
Event	25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017 - Kuantan, Pahang, Malaysia Duration: 27 Aug 2017 → 29 Aug 2017

Publication series

Name	AIP Conference Proceedings
Volume	1974
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017
Country/Territory	Malaysia
City	Kuantan, Pahang
Period	27/08/17 → 29/08/17

Keywords

Laplace transform
Volterra integral equation
aggregate discounted claim
copula

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10.1063/1.5041641

Cite this

Ramli, S. N. M., Rozali, N. A. M., Alhabshi, S. F. S. Y., & Hashim, I. (2018). Laplace transform on the recursive moments of copula-dependent aggregate discounted claims. In H. Maidinsah, S. R. Sharif, W. E. Z. W. A. Rahman, A. B. Akbarally, M. Mohamed, D. Mohamad, & M. M. Jaffar (Eds.), Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence Article 020110 (AIP Conference Proceedings; Vol. 1974). American Institute of Physics Inc.. https://doi.org/10.1063/1.5041641

Ramli, Siti Norafidah Mohd ; Rozali, Nur Atikah Mohamed ; Alhabshi, Sharifah Farah Syed Yusoff et al. / Laplace transform on the recursive moments of copula-dependent aggregate discounted claims. Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence. editor / Hamidah Maidinsah ; Sarifah Radiah Sharif ; Wan Eny Zarina Wan Abdul Rahman ; Ajab Bai Akbarally ; Mesliza Mohamed ; Daud Mohamad ; Maheran Mohd Jaffar. American Institute of Physics Inc., 2018. (AIP Conference Proceedings).

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abstract = "We consider the recursive moments of aggregate discounted claims, where the dependence between the inter-claim time and the subsequent claim size is captured by a copula distribution. The equations of the recursive moments, which take the form of the Volterra integral equation (VIE), are then solved using the Laplace transform. We then compute its mean and variance, and compare with the results obtained in previous literature.",

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doi = "10.1063/1.5041641",

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series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

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Ramli, SNM, Rozali, NAM, Alhabshi, SFSY & Hashim, I 2018, Laplace transform on the recursive moments of copula-dependent aggregate discounted claims. in H Maidinsah, SR Sharif, WEZWA Rahman, AB Akbarally, M Mohamed, D Mohamad & MM Jaffar (eds), Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence., 020110, AIP Conference Proceedings, vol. 1974, American Institute of Physics Inc., 25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017, Kuantan, Pahang, Malaysia, 27/08/17. https://doi.org/10.1063/1.5041641

Laplace transform on the recursive moments of copula-dependent aggregate discounted claims. / Ramli, Siti Norafidah Mohd; Rozali, Nur Atikah Mohamed; Alhabshi, Sharifah Farah Syed Yusoff et al.
Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence. ed. / Hamidah Maidinsah; Sarifah Radiah Sharif; Wan Eny Zarina Wan Abdul Rahman; Ajab Bai Akbarally; Mesliza Mohamed; Daud Mohamad; Maheran Mohd Jaffar. American Institute of Physics Inc., 2018. 020110 (AIP Conference Proceedings; Vol. 1974).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Hashim, Ishak

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N2 - We consider the recursive moments of aggregate discounted claims, where the dependence between the inter-claim time and the subsequent claim size is captured by a copula distribution. The equations of the recursive moments, which take the form of the Volterra integral equation (VIE), are then solved using the Laplace transform. We then compute its mean and variance, and compare with the results obtained in previous literature.

AB - We consider the recursive moments of aggregate discounted claims, where the dependence between the inter-claim time and the subsequent claim size is captured by a copula distribution. The equations of the recursive moments, which take the form of the Volterra integral equation (VIE), are then solved using the Laplace transform. We then compute its mean and variance, and compare with the results obtained in previous literature.

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Ramli SNM, Rozali NAM, Alhabshi SFSY, Hashim I. Laplace transform on the recursive moments of copula-dependent aggregate discounted claims. In Maidinsah H, Sharif SR, Rahman WEZWA, Akbarally AB, Mohamed M, Mohamad D, Jaffar MM, editors, Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence. American Institute of Physics Inc. 2018. 020110. (AIP Conference Proceedings). doi: 10.1063/1.5041641

Laplace transform on the recursive moments of copula-dependent aggregate discounted claims

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