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All Journal AKSIOMA: Jurnal Program Studi Pendidikan Matematika JIPM (Jurnal Ilmiah Pendidikan Matematika) Math Didactic: Jurnal Pendidikan Matematika Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) Unisda Journal of Mathematics and Computer Science (UJMC) Transformasi : Jurnal Pendidikan Matematika dan Matematika JATI EMAS (Jurnal Aplikasi Teknik dan Pengabdian Masyarakat) Jurnal Teknik Informatika (JUTIF) Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Differential: Journal on Mathematics Education
Feby Indriana Yusuf
Universitas PGRI Banyuwangi
Humanities Computer Science & IT Education Engineering Mathematics Public Health Other

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Journal : Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi

 1 
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.
Implementasi Metode Bayesian untuk Menghitung Premi Produk Asuransi Kendaran Bermotor dengan Pendekatan Monte Carlo Markov Chain Situmorang, Boy Nathanael; A’la, Kevina Alal; Arvianti, Aurellia; Yusuf, Feby Indriana; Handamari, Endang Wahyu
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Volume 13 Issue 2 August 2025
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v13i2.32930

Abstract

Accurate premium determination is a fundamental aspect of risk management in motor vehicle insurance. This study implements the Bayesian method using a Markov Chain Monte Carlo (MCMC) approach to calculate the net premium. The aggregate claim model is constructed from a claim frequency distribution (Poisson) and a claim severity distribution (Generalized Extreme Value (GEV)), with the GEV distribution specifically chosen to model extreme claim risk. The analysis utilizes generated data for the period 2018–2024, with parameters derived from the historical data of PT Asuransi Jasa Indonesia Purwokerto (2013–2017). Parameter estimation, performed via OpenBUGS software, was validated to have achieved good convergence (MC-error   ). Based on the estimated parameters, a premium of IDR 397.502.000 was obtained, calculated using the net premium principle from the expected value of aggregate claims. These results demonstrate that the Bayesian MCMC approach is effective for producing a robust premium estimation, contributing a pricing framework that explicitly accounts for extreme value claims.
Co-Authors Adi, Puti Zakiyah Raisa Anggraini, Dessy Anggraini, Dessy Anjasari, Dwi Hilda Anjasari, Dwi Hilda Arvianti, Aurellia A’la, Kevina Alal Barep Yohanes Bukhori, Hilmi Aziz Dwi Hilda Anjasari Dwi Mifta Mahanani, Dwi Mifta Dzurotul Mutimmah Eko Listiwikono Endang Wahyu Handamari Fitri Nurmasari Hady Rasikhun Heri Susanto Imam Nurhadi Purwanto Julianti, Nurma Haya Nada, Qothrun Nadya Adharani Novi Prayekti Nurma Haya Julianti Permata, Wahyu Finda Permata, Wahyu Finda Rachmaniah Mirza Hariastuti Rahmi, Miftachul Rahmi, Miftachul Saiful Bukhori Saragih, Trecy Elisabet Tioralina Sari, Meylita Situmorang, Boy Nathanael Sulistiono Susanti, Reny Eka Evi Syaiful Anam Wiwik Handayani