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Nurul Gusriani
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Universitas Padjadjaran
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Pemodelan Indeks Pembangunan Manusia di Kalimantan Timur Menggunakan Spasial Durbin Data Panel Kaerudin, Nandira Putri; Gusriani, Nurul; Ruchjana, Budi Nurani
Jurnal Matematika Integratif Vol 20, No 1: April 2024
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v20.n1.55158.101-115

Abstract

Indeks Pembangunan Manusia (IPM) merupakan salah satu indikator yang dapat digunakan untuk mengukur kemajuan suatu negara. Di Indonesia sendiri masih terdapat ketimpangan IPM antar provinsinya. Provinsi Kalimantan Timur merupakan salah satu provinsi yang memiliki rata-rata IPM tinggi di Indonesia, sehingga perlu dilakukan studi mengenai IPM untuk memberikan gambaran bagi provinsi dengan IPM rendah. IPM di suatu wilayah dipengaruhi oleh wilayah sekitarnya, hal ini disebabkan oleh efek spasial. Analisis regresi spasial merupakan metode yang mampu mengakomodasi efek spasial. Spatial Durbin Model (SDM) adalah salah satu pengembangannya. Selain itu, penggunaan data panel pada model menyebabkan variabilitas pada data. Penelitian ini bertujuan untuk memodelkan IPM di Kalimantan Timur menggunakan spasial durbin data panel meliputi lima kategori: Persentase penduduk miskin; Tingkat Partisipasi Angkatan Kerja (TPAK); Persentase penduduk; Angka Partisipasi Murni (APM); Persentase rumah tangga menurut fasilitas toilet sendiri. Berdasarkan hasil uji Hausman dan Chow, terdapat efek tetap pada setiap kabupaten/kota sehingga FEM merupakan jenis data panel yang digunakan. Selain itu, Hasil uji Moran’s I mengindikasikan adanya dependensi spasial positif dalam data IPM. Koefisien determinasi pada model spasial Durbin data panel menunjukkan nilai 99,92417% yang berarti model ini baik digunakan untuk memodelkan IPM di Kalimantan Timur.
Estimation of Labor Force Participation Rate (TPAK) in Java's Data-Scarce Areas Using Ordinary Cokriging Angelina, Sofia; Gusriani, Nurul; Firdaniza, Firdaniza
Jurnal Matematika Integratif Vol 21, No 2: Oktober 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n2.65239.229-244

Abstract

The quality of the labor force is crucial for economic development, and the Labor Force Participation Rate (TPAK) is a key employment indicator. In 2024, TPAK data collection in Java Island faced gaps in DKI Jakarta and Banten Provinces, limiting comprehensive labor mapping. To overcome this, spatial estimation methods are needed using data from surrounding areas and auxiliary variables. The Open Unemployment Rate (TPT) has a strong inverse relationship with TPAK, each 1\% TPAK increase lowers TPT by 14,82\%, making it a suitable auxiliary variable. This study estimates the 2024 TPAK for DKI Jakarta and Banten using the ordinary cokriging method, with TPT as the secondary variable. Spatial autocorrelation analysis confirmed that TPAK and TPT exhibit spatial patterns, are normally distributed, and meet stationarity assumptions. The best cross semivariogram model was identified using k-fold cross validation, which selected the spherical model with the lowest average RMSE of 4,24. The resulting ordinary cokriging model accurately predicted TPAK values, achieving a MAPE of 3,25\%. These estimates enable spatial visualization of TPAK in previously unobserved areas, contributing to a more complete understanding of labor participation across Java Island.
Struktur Aljabar untuk Barisan Kodon dari Asam Deoksiribonukleat (DNA) Hasan, Nabila Nurmala; Kurniadi, Edi; Gusriani, Nurul
Jurnal Matematika Integratif Vol 21, No 2: Oktober 2025
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v21.n2.67778.213-228

Abstract

This article discusses the algebraic structure of codon sequences as a representation of DNA nitrogen base sets in mathematical terms. The study aims to prove what algebraic structures are obtained for codon sequences from DNA bases. The methods used include qualitative research methods in the form of literature studies and quantitative research methods in the form of experiments on DNA base sets. In mathematical notation, the nitrogen bases of DNA can be collected in a set and connected into algebraic structures through a bijective mapping on the Galois field of order 4. This results in the set B being viewed as a Galois field of order 4. Additionally, DNA base triplets or codons can be represented in mathematical form. Furthermore, these codons are bijectively mapped onto the Galois field of order 64, so that the resulting algebraic structure is a field. The result of this study show that the codon sequences have an algebraic structure in the form of a one-dimensional vector space over the Galois field on the codon. For further research, the Lie structure in codon can be investigated through the construction of its Lie brackets, where this vector space is a necessary condition for Lie algebras.
Analysis of Term Life Insurance Premium Reserves Using the Zillmer Method with Hull–White Interest Rates Fatahillah Akmal; Riaman; Gusriani, Nurul
International Journal of Business, Economics, and Social Development Vol. 7 No. 2 (2026): International Journal of Business, Economics, and Social Development (IJBESD)
Publisher : Rescollacom (Research Collaborations Community)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijbesd.v7i2.1172

Abstract

This study analyzes the valuation of premium reserves for term life insurance using the Zillmer method under a stochastic interest rate framework. In conventional actuarial practice, premium reserves are commonly calculated using deterministic interest rate assumptions, which may inadequately reflect the dynamic nature of interest rate movements over long-term policy horizons. To address this limitation, this study applies the one-factor Hull–White interest rate model to incorporate stochastic interest rate dynamics into the reserve calculation process. The Hull–White model parameters are estimated using historical interest rate data, and interest rate paths are generated through numerical simulation. These simulated interest rates are then employed to compute discount factors in the calculation of Zillmer premium reserves. The analysis focuses on illustrating how stochastic interest rate movements influence the development of premium reserves over the policy duration, rather than on probabilistic risk measurement or capital adequacy assessment. The results show that premium reserves calculated under the stochastic interest rate framework exhibit dynamic patterns over time, particularly during the early and middle policy periods. Compared to deterministic interest rate assumptions, the stochastic approach captures variations in reserve values arising from interest rate fluctuations. This finding highlights the sensitivity of Zillmer premium reserves to interest rate dynamics. Overall, this study demonstrates that integrating the Hull–White stochastic interest rate model with the Zillmer method provides a descriptive and flexible framework for analyzing premium reserves in term life insurance. The proposed approach may serve as a basis for further research on stochastic valuation methods in actuarial applications.
Clustering of Banking Sector Stocks using Integration of Fourier Transform, Spectral Clustering, and Fuzzy C-Means as a Basis for Mean-Variance Portfolio Optimization Ricardo, Dimitri Salsabila Fakhriyah; Gusriani, Nurul; Napitupulu, Herlina
Jurnal Matematika Integratif Vol 22, No 1: April 2026
Publisher : Department of Matematics, Universitas Padjadjaran

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24198/jmi.v22.n1.69287.59-72

Abstract

The Indonesian capital market has experienced significant growth accompanied by high volatility, particularly in the banking sector whichholds a substantial contribution to market capitalization. Extremevolatility during the 2019-2024 period triggered by the impact of theCOVID-19 pandemic, economic recovery phases, and global macroeconomic challenges has created complexities in investment decisionmaking and portfolio optimization, which often produces unstable solutions under uncertain market conditions. Various studies have applied frequency domain analysis to uncover hidden patterns in stockprice movements or clustering to group stocks based on their characteristics to support optimal investment decision-making, however theintegration of these two approaches remains limited in its application togenerate robust portfolio optimization solutions in the Indonesian capital market. This study aims to generate clustering of banking sectorstocks through the integration of Fourier Transform, spectral clustering, and Fuzzy C-Means and to construct an optimal portfolio using theMean-Variance method based on the clustering results. This study usesclosing price data of 41 banking sector stocks on the Indonesia StockExchange for the 2019-2024 period through an integrated approach ofFourier Transform to extract frequency patterns, spectral clustering asa basis for grouping, Fuzzy C-Means to generate cluster membership degrees, and Mean-Variance for portfolio optimization. The results showthat the integration of these methods produces four optimal stock clusters consisting of nine stocks with a medium risk-low return profile,six stocks with a high risk-high return profile, fifteen stocks with a lowrisk-low return profile, and eleven stocks with a medium risk-high return profile. Based on the clustering results, four representative stockswere selected from each cluster for portfolio optimization, resulting inan optimal portfolio at a risk aversion value of ρ = 6.83 with a portfolio ratio of 3.4128877. This optimal portfolio is constructed from fourrepresentative stocks with weight allocations of 11.48% BMAS, 11.76%ARTO, 72.08% BNGA, and 4.68% BBHI, with an expected return valueof 0.0263613 and a portfolio variance of 0.0077241.
Co-Authors Angelina, Sofia Anita Triska Arif Rahman Aulia Wanda Puspitasari Azzahra, Rediva Badrulfalah Badrulfalah Bagariang, Elizabeth Irene Balqis, Viona P Betty Subartini Budi Nurani Ruchjana Clarita Simar DHEA ARIESTA Diah Chaerani Dianne Amor Kusuma Edi Kurniadi Edi Kurniadi Endang Rusyaman Fatahillah Akmal Ferdian Agustiana Firdaniza Firdaniza Ghiffari, Alif Muhamad Gumgum Darmawan Hasan, Nabila Nurmala Herlina Napitupulu Iin Irianingsih Irmansyah, Athaya Zahrani Jaka Nazarudin Kaerudin, Nandira Putri Kankan Parmikanti Kartika Dewi Luthfi Ghiffari Melda Noereast Talytha Michelle Selina Buntara Milani Destriana Mohamad Nurzaman Muslihin, Khoirunnisa R A Nabila Putri Nasri, Ramadhoni Natalia Syafitri Kustanto Nurhadini Putri Nursanti Anggriani Ramdhani, Muhammad Dhafin Qinthar Rediva Azzahra Reffa Ayu Anggraeni Reffa Ayu Anggraeni Riaman Ricardo, Dimitri Salsabila Fakhriyah Rizal Amegia Saputra Ruslan Ruslan Samantha Surya Saprilian Hidayat Satyaputra, Ida Bagus Wira Krishna Sri Rahayu Sunarta Susanto Sussy Susanti Syifana, Hani Tiara Aprilia K Tiara Aprilia K, Tiara Tomy Perdana Wahyu, Azkanul