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Romantica, Krishna Prafidya
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Endowment Life Insurance Calculation Modeling with DARA Utility Function and Stochastic Interest Leo, Jason Filbert; Romantica, Krishna Prafidya; Johan, Arsyelina Husni
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 11 No. 1 (2026): Mathline : Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v11i1.993

Abstract

In this research, a 10-year endowment life insurance’s premium will be calculated with a DARA function according to principle of utility equivalence. The calculation results will be performed using a Vasicek interest-based model, among male and female policyholders within the age range of 20-80 years old, and over varying benefit levels. Indonesian Mortality Table IV 2019 is used as reference for mortality data. Stochastic interest is modeled using the Vasicek Model derived through Ordinary Least Square Method (OLS) Method from BI-Rate in the volatile September 2022 - August 2024 period with a monthly step time, which yields the following parameters: , , , resulting in a 95% confidence interval  with standard error . This  indicated high uncertainty in the interest modelling. The results showed that premium rate is heavily affected by this volatility in the interest rates. Premium value is higher for male than female policyholders and it increases faster at higher entry age due to an increase of the mortality rate. The relation between the DARA coefficient and premium value is non-linear despite a slight increase in premium when a larger coefficient is chosen. An increase of benefit rate is followed by a nearly proportional increase of the premium rate. Further research on this topic could analyze the impact of policy horizon and wealth on the premium rate or compare the results with another stochastic model (e.g. CIR model).
An Integer Linear Programming Model for Diagnosing Unmastered Mathematical Topics Based on Bloom's Cognitive Domains Irvan, Irvan; Romantica, Krishna Prafidya; Azis, Zainal; Harahap, Tua Halomoan
Indonesian Journal of Education and Mathematical Science Vol 7, No 2 (2026)
Publisher : Universitas Muhammadiyah Sumatera Utara (UMSU)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30596/ijems.v7i2.27150

Abstract

This study aims to develop a mathematical model based on Integer Linear Programming (ILP) to map unmastered mathematical topics among senior high school students according to the cognitive domains of Bloom's Taxonomy, namely Knowledge (C1), Comprehension (C2), and Application (C3). The research method employed a quantitative approach, utilizing test result data from a 48-item instrument covering 16 mathematical subtopics, administered to 147 twelfth-grade students in the Natural Science program. The data were analyzed using LINDO 6.1 software to generate a profile of student mastery for each subtopic and cognitive domain. The results indicate that student mastery was generally higher in the Knowledge (C1) domain, with eight subtopics achieved, compared to the Comprehension (C2) domain with six subtopics and the Application (C3) domain with five subtopics. Out of the total 48 test items, only 19 items (39.6%) were mastered by the students, while 29 items (60.4%) were not. The Equations and Inequalities (X2) subtopic was the only material not mastered across all three domains. These findings suggest the need for learning strategies that place greater emphasis on strengthening conceptual understanding and contextual application. The application of the ILP model in this study proves effective as a diagnostic tool for identifying student weaknesses in a detailed and objective manner, thereby serving as a reference for teachers in designing targeted remedial programs. Furthermore, this model has the potential to be replicated in other schools to continuously monitor the development of student proficiency.
Co-Authors Agung Nugraha Amigo, Royyan Andriani, Rosa Ani Nuraini Anuraga Jayanegara Azis, Zainal Gentari, Putu Tika Dinda Hasvi, Ismail Heri Kurniawan, Heri Husni Johan, Arsyelina Iriani Tarigan, Asmara Irvan Irvan Johan, Arsyelina Husni Leo, Jason Filbert Mariss, Diajeng Banowati Martinasari, Made Diyah Putri Naili Muna, Siti Umamah Paiz Jalaludin Putri Martinasari, Made Diyah Rahman, Alrafiful Tri Wijayanti Septiarini Tua Halomoan Harahap, Tua Halomoan