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Rahmi, Emli
Universitas Negeri Gorontalo
Arts Civil Engineering, Building, Construction & Architecture Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Environmental Science Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Public Health Social Sciences

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Calculation of Annual Premiums and Premium Reserves for Endowment Joint Life Insurance Based on Stochastic Interest Rates Using the Monte Carlo Method Bela Cintiya Samwan; Agusyarif Rezka Nuha; Armayani Arsal; Emli Rahmi; La Ode Nashar
Jurnal Multidisiplin Sahombu Vol. 6 No. 01 (2026): Jurnal Multidisiplin Sahombu, January 2026
Publisher : Sean Institute

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Abstract

This study examines the determination of annual premiums and premium reserves for an endowment joint life insurance product by incorporating interest rate uncertainty through the Cox-Ingersoll-Ross (CIR) stochastic model and Monte Carlo simulation. The Indonesian Mortality Table 2023 is used to compute joint survival probabilities for the three insured individuals, while the CIR parameters are estimated from historical interest rate data for the period 2020-2024. The present value of benefits and annuities is calculated along each simulated path, enabling the premium and premium reserves to be evaluated prospectively based on fluctuating interest rate dynamics. The results show that the magnitude of premiums and reserves is influenced by the initial ages of the insured, the mortality structure, the sum assured, and the variability of the simulated interest rates. At the beginning of the contract, all scenarios produce negative reserves because accumulated premiums are still insufficient to cover the expected present value of benefits. However, the reserves increase steadily over time and turn positive toward the end of the insurance term. These findings indicate that the Monte Carlo approach based on the CIR model provides a more adaptive and realistic representation of premium and reserve behavior compared with deterministic methods, thereby supporting more accurate financial risk assessment for insurance companies.
Penerapan Metode Fuzzy Time Series Chen Orde Tinggi Pada Peramalan Nilai Tukar Petani Provinsi Gorontalo Muhammad, Nur Miftah; Hasan, Isran K.; Arsal, Armayani; Rahmi, Emli; Nashar, Laode
Jurnal Riset Mahasiswa Matematika Vol 5, No 4 (2026): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v5i4.41337

Abstract

Nilai Tukar Petani (NTP) merupakan salah satu indikator ekonomi yang digunakan untuk menggambarkan tingkat kesejahteraan petani dan kondisi sektor pertanian. Pergerakan nilai NTP yang bersifat fluktuatif memerlukan pendekatan peramalan yang mampu menangkap pola data secara memadai. Penelitian ini bertujuan menerapkan metode Fuzzy Time Series (FTS) Chen orde tinggi untuk meramalkan Nilai Tukar Petani di Provinsi Gorontalo serta mengidentifikasi model orde yang memberikan tingkat kesalahan peramalan yang paling tepat. Data yang digunakan berupa data bulanan NTP Provinsi Gorontalo periode Januari 2020 hingga Oktober 2025 yang terdiri dari 70 observasi dan diperoleh dari publikasi resmi Badan Pusat Statistik. Data dibagi menjadi 80% data latih dan 20% data uji menggunakan pendekatan pembagian berdasarkan waktu. Tahapan analisis meliputi penentuan himpunan semesta, pembentukan interval, proses fuzzifikasi, pembentukan Fuzzy Logical Relationship (FLR) dan Fuzzy Logical Relationship Group (FLRG), defuzzifikasi, serta evaluasi kinerja model menggunakan Mean Absolute Percentage Error (MAPE). Hasil analisis menunjukkan bahwa model FTS Chen orde dua menghasilkan nilai MAPE sebesar 3,3164% pada data uji, yang lebih kecil dibandingkan dengan model orde satu. Sementara itu, model orde tiga tidak dapat digunakan secara optimal karena tidak terbentuk hubungan fuzzy pada beberapa periode data pengujian. Hasil ini menunjukkan bahwa pendekatan FTS Chen orde dua dapat memberikan hasil peramalan yang relatif lebih baik pada data NTP yang dianalisis dalam penelitian ini.
Co-Authors Abdussamad, Trizaning Nursahbani Agusyarif Rezka Nuha Ahaya, Sitty Oriza Sativa Putri Aliwu, Randa Resvitasari Armayani Arsal Beay, Lazarus Kalvein Bela Cintiya Samwan Biduli, Meiske DIAN SAVITRI Djihad Wungguli Gani, Friansyah Hasan S. Panigoro Hidayanti, Sri Amalia Ibrahim, Rusdianto Isran K Hasan Karim, Finansiya S. Abd. Kasim, Ranan La Ode Nashar Lailany Yahya Mahmud, Sri Lestari Muhammad, Nur Miftah Nadiyyah, Ana Nashar, Laode NISKY IMANSYAH YAHYA Novianita Achmad Nurhalis Hasan Nurwan Nurwan Nurwan, Nurwan Resmawan Resmawan Reza Mokodompit Salmun K. Nasib Sidik, Amelia Tri Rahma Siti Maisaroh Siti Nurmardia Abdussamad