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All Journal Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Indonesian Actuarial Journal
Saragih, Trecy Elisabet Tioralina
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Mathematics Physics

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Penerapan Collective Risk Model dalam Penentuan Premi Asuransi Bencana Alam Yusuf, Feby Indriana; Adi, Puti Zakiyah Raisa; Saragih, Trecy Elisabet Tioralina
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 12 Issue 2 December 2024
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v12i2.28632

Abstract

Indonesia is prone to natural disasters such as volcanic eruptions, earthquakes, and tsunamis due to tectonic activity involving the Indo-Australian and Eurasian plates. Therefore, the government introduced natural disaster insurance in 2018 to mitigate financial losses caused by such events. This study employs the Collective Risk Model (CRM) to determine premium rates. The Poisson process and Gamma distribution are utilized to estimate the frequency and severity of natural disasters. Estimation is performed using Maximum Likelihood Estimation (MLE), while premiums are calculated based on the expected value and variance of aggregate risk using the Expected Value Principle and the Standard Deviation Principle. The results show that the expected value and variance of claim frequency are both . Furthermore, claims for losses follow the Gamma distribution, with an expected value and variance of  and . The mean and variance of aggregate claims are Rp  and Rp . The Standard Deviation Principle produces lower premiums than the Expected Value Principle under the same loading factor.
Advancing Sharia Insurance Product for Natural Disaster Risks: A Collective Risk Model Approach Saragih, Trecy Elisabet Tioralina; Lintang, Alfonsius; Sinaga, Chintya Luminar
Indonesian Actuarial Journal Vol. 1 No. 1 (2025): Indonesian Actuarial Journal
Publisher : Persatuan Aktuaris Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Sharia insurance (takaful) serves as a means to promote solidarity and shared responsibility, helping protect individuals from unexpected risks by transferring or minimizing these risks through coverage provided by insurance companies. Sharia insurance is grounded in the concept of ta’awun which leads to mutual assistance and aims to eliminate forbidden elements in conventional insurance practices such as interest (riba), uncertainty (gharar), and gambling (maysir). Although interest rates are not used to calculate the present value of benefits, sharia insurance products can be improved through actuarial modelling based on expected risk levels and historical data. This paper creates a sharia insurance model for natural disasters of floods and earthquakes using the Collective Risk Model (CRM), with natural disaster frequency data distributed Poisson and natural disaster loss amounts distributed Weibull 3-Parameters. The result reflects the contribution value calculated using the expectation principle and standard deviation of total natural disaster losses. This study also provides a mathematical table as a model for applying the CRM’s contribution value to sharia insurance for natural disasters of floods and earthquakes. This table will detail how funds contributed by policyholders are managed, including the percentages allocated to personal accounts, the tabarru’ (donation) account, and ujrah (management fees), as well as the amounts of profit and benefits accrued to policyholders. This breakdown aims to promote transparency and fairness in shariah-compliant insurance for companies and policyholders, ensuring that fund contributions are managed equitably.
Co-Authors Adi, Puti Zakiyah Raisa Feby Indriana Yusuf Lintang, Alfonsius Sinaga, Chintya Luminar