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All Journal Jurnal Penyuluhan FORUM STATISTIKA DAN KOMPUTASI Forum Pasca Sarjana CAUCHY: Jurnal Matematika Murni dan Aplikasi Al-Jabar : Jurnal Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Mathematics Jambura Geoscience Review InPrime: Indonesian Journal Of Pure And Applied Mathematics Jurnal Statistika dan Matematika (Statmat) Jurnal Statistika dan Aplikasinya Makara Human Behavior Studies in Asia Milang Journal of Mathematics and Its Applications Jurnal Matematika Integratif MILANG Journal of Mathematics and Its Applications Limits: Journal of Mathematics and Its Applications
I Gusti Putu Purnaba
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Institut Pertanian Bogor
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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PREMI BERSIH TAHUNAN ASURANSI JIWA BERJANGKA UNTUK KASUS MULTIPLE DECREMENT DENGAN VARIASI SUKU BUNGA Adilla, Indrya; I Gusti Putu Purnaba; Ruhiyat; Berlian Setiawaty; Windiani Erliana; Septyanto, Fendy
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 2 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.18.2.139-153

Abstract

Aplikasi penggunaan model multiple decrement terdapat pada asuransi jiwa dengan tambahan manfaat dan dana pensiun. Manfaat dibayarkan bergantung pada penyebab keluarnya peserta dari asuransi. Untuk menentukan besar premi dan nilai manfaat pada suatu waktu diperlukan data Tabel Penyusutan Jamak dan asumsi suku bunga. Penelitian ini bertujuan untuk mengkonstruksi Tabel Penyusutan Jamak dari data Illustrative Service Table yang tersedia di library software R dan menentukan besar premi bersih tahunan asuransi jiwa berjangka 35 tahun untuk seseorang yang berusia 30 tahun yang memberikan manfaat kematian, mengundurkan diri, cacat permanen, dan pensiun dengan variasi suku bunga. Menggunakan suku bunga konstan diperoleh besar premi bersih tahunan dari 3.5% sampai 15% akan menurun semakin bertambahnya suku bunga, namun kembali meningkat dari suku bunga 15% hingga 20%. Besar premi bersih tahunan dengan asumsi suku bunga bervariasi mengikuti besar suku bunga nominal Republik Korea (yang telah dimodifikasi) lebih kecil dibandingkan dengan premi ketika diasumsikan suku bunga konstan sebesar rata-rata suku bunga nominal tersebut.
PENENTUAN PREMI DAN CADANGAN MANFAAT ASURANSI JIWA JOINT LIFE SAAT TINGKAT BUNGA DIMODELKAN DENGAN COX-INGERSOLL-ROSS Yuda Ardiansyah; Windiani Erliana; Ruhiyat; I Gusti Putu Purnaba; Fendy Septyanto
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 1 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.1.23-41

Abstract

Pada karya ilmiah ini dibahas asuransi jiwa joint life untuk tiga orang tertanggung dengan tingkat bunga model Cox-Ingersoll-Ross (CIR). Manfaat dari asuransi jiwa tersebut dibayarkan setelah tahun kesepuluh jika tidak ada kematian terjadi, kematian pertama, atau kematian kedua pada peserta asuransi. Tingkat bunga yang digunakan dalam karya ilmiah ini adalah tingkat bunga BI 7-day (Reverse) Repo Rate (BI7DRR) periode September 2016 sampai September 2022 yang dimodelkan dengan model CIR. Parameter model CIR diduga dengan metode Ordinary Least Square. Model tingkat bunga tersebut digunakan dalam penghitungan premi bersih dan cadangan manfaat asuransi jiwa joint life berdasarkan Tabel Mortalitas Indonesia 2019. Hasil menunjukkan bahwa tingkat bunga BI7DRR dapat dimodelkan dengan baik dengan model CIR. Selain itu, semakin tua usia peserta saat mendaftar asuransi, maka semakin tinggi pembayaran premi bersih, sedangkan cadangan manfaat semakin rendah.
PERAMALAN NILAI TUKAR RUPIAH TERHADAP DOLAR SINGAPURA, BAHT, DAN PESO MENGGUNAKAN METODE GSTAR Budiarti, Retno; Rahmawati, D. S.; Septyanto, Fendy; Purnaba, I Gusti Putu
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.20.1.1-13

Abstract

The Generalized Space-Time Autoregressive (GSTAR) model is an extension of the Space-Time Autoregressive (STAR) model. The difference between the two models lies in the parameter assumptions. In the STAR model, the parameters are assumed to be independent of location, so this model is only suitable for data with homogeneous locations. Meanwhile in the GSTAR model, the parameters are assumed to change for each different location. This research aims to develop the best model for forecasting the Rupiah exchange rate against the Singapore Dollar, Thai Baht, and Philippine Peso. The appropriate model used for the Rupiah exchange rate data is the GSTAR(51)I(1) model. The weights used in this study are uniform location weights and inverse distance. The modeling results show that the best model is the model with inverse distance weighting, which has an MSE value of 371.8907 with MAPE values for each of the Rupiah exchange rate data against the Singapore Dollar, Thai Baht, and Philippine Peso of 0.3154214%, 0.8369436%, and 0.6237245%, respectively.
ANALISIS HUBUNGAN HARGA EMAS DAN PASAR SAHAM MENGGUNAKAN MIXED-COPULAS Budiarti, Retno; Sulaiman, Muhammad Yusuf; Purnaba, I Gusti Putu; Erliana, Windiani; Setiawaty, Berlian; Ruhiyat
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.20.1.15-29

Abstract

Gold is considered as a reliable investment tool for long-term savings and/or investment portfolios. Investors who do not like high risks trust gold to be a safe haven commodity that can mitigate the impact of any financial crisis. Gold and stocks are often used as substitutes for each other, where the two have an inverse relationship. Copula is used to capture the dependence relationship between world gold prices and the stock indexes. The data used are the stock index data for the JKSE Indonesia), PSE (Phillipines), Nikkei 225 (Japan), HSI (Hong Kong), and world gold prices (XAU) from January 1, 2014 to December 31, 2019. From the data, the ARMA-GARCH model is made to solve the problem of autocorrelation and heteroscedasticity. Then, the correlation between assets is calculated using the rank correlation. Furthermore, four pairs of data are made from each stock index with the price of gold. Next, the best copula and the estimated Value-at-Risk (VaR) are sought for each portfolio. From the results of the selecting of the best copula for each pair of data, it is found that gold can be a safe haven asset in the Hong Kong's stock market. The VaR results show that the biggest loss is in the Japanese market.
ANALISIS SURVIVAL PASIEN INSUFFICIENCIA CORDIS MENGGUNAKAN MODEL REGRESI WEIBULL DAN MODEL REGRESI COX PROPORTIONAL HAZARD Dwi Fidiana; Budiarti, Retno; I Gusti Putu Purnaba; Nur Agustiani
MILANG Journal of Mathematics and Its Applications Vol. 21 No. 1 (2025): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.21.1.45-59

Abstract

Analisis survival digunakan untuk mengevaluasi durasi waktu dari awal pengamatan hingga terjadinya suatu peristiwa, seperti kesembuhan atau kematian. Penelitian ini memfokuskan pada pasien insufficiencia cordis. Analisis dilakukan dengan pendekatan parametrik (regresi Weibull) serta semi-parametrik (Cox Proportional Hazard). Model regresi Weibull menjadi model terbaik dengan nilai AIC 127,50 dan MSE 0,5071. Variabel signifikan yang memengaruhi analisis survival pada penelitian ini adalah age, ejection fraction, serum sodium, platelets, dan serum creatinine. Penelitian ini memberikan kontribusi signifikan bagi dunia medis dan industri asuransi, memungkinkan identifikasi faktor risiko yang lebih akurat dan mendukung pengambilan keputusan dalam strategi penanganan medis serta penetapan premi asuransi yang berbasis risiko.
Modelling Dependencies of Stock Indices During Covid-19 Pandemic by Extreme-Value Copula Budiarti, Retno; Intansari, Kumala; Purnaba, I Gusti Putu; Septyanto, Fendy
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 3 (2023): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i3.15109

Abstract

Quantifying dependence among variables is the core of all modelling efforts in financial models. In the recent years, copula was introduced to model the dependence structure among financial assets return, and its application developed fast. A large number of studies on copula have been performed, but the study of multivariate extremes related with copulas was quite behind in comparison with the research on copulas. The COVID-19 pandemic is an extreme event that has caused the collapse of various economic activities which resulted in the decline of stock prices. The modelling of extreme events is therefore important to mitigate huge financial losses. Extreme-value copula can be suitable to quantify dependencies among assets under an extreme event. In this paper, we study the modelling of extreme value dependence using extreme value copulas on finance data. This model was applied in the portfolio of the IDX Composite Index (IHSG), Straits Times Index (STI) and Kuala Lumpur Stock Exchange (KLSE). Each individual asset return is modelled by the ARMA-GARCH and the joint distribution is modelled using extreme value copulas. This empirical study showed that Gumbel copula is the most appropriate extreme value copulas for the three indices. The results of this study are expected to be used as a basis for investors in the formation of a portfolio consisting of 2 financial assets and a portfolio consisting of 3 financial assets. 
Determining Tomato Crop Agricultural Insurance Premium for COVID-19 Pandemic Setyawan, Binar Aulia; Purnaba, I Gusti Putu; Budiarti, Retno
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v8i2.22782

Abstract

One type of insurance known as parametric insurance has an agreement for predetermined events made at the beginning of the contract between the insurer (insurance firm) and the insured (farmer). When the causative event occurs, the provision applies that insurer must pay insured with some amount of money (damage compensation). Ozaki has formulated parametric method of premium rates for agricultural insurance build upon yields in specific area. Indonesian Ministry of Agriculture uses this method to ensure that farmers can re-plant crops in following planting season if a crop failure occurs. However, the COVID-19 pandemic's losses were not covered by this method. Given this, we would like to develop agricultural insurance models for tomato crops which figure out COVID-19 pandemic. For make it easier to see the price of tomato commodity due to impact of COVID-19 pandemic, in this research we will take a case study on agriculture managed by PT Mitra Tani Parahyangan. This company is engaged in the horeca business, so it has been greatly affected by the quarantine policy. The results of this study are suggestions for policy makers in anticipation if a pandemic occurs again, it help farmers and Indonesia’s food availability will be maintained.
Comparison of the Actuarial Model for A Normal Lumpsum Pension Plan Using Defined-Benefit and Hybrid Models of Company Employees Maharani, Ardella; Purnaba, I Gusti Putu; Ruhiyat, Ruhiyat
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 2 (2023)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v5i2.32741

Abstract

AbstractIn this research, we delve into the realm of pension plan programs, essential for securing a robust livelihood post-retirement through the provision of pension benefits to retired employees. Addressing the intricate balance between financial sustainability and risk mitigation, companies are mandated to allocate funds for pension benefits. The hybrid pension plan, a novel amalgamation of defined-benefit (DB) and defined-contribution (DC) features, emerges as a strategic solution to minimize the inherent risks of both models. This study undertakes the task of calculating the costs associated with pension benefits and the replacement ratio (RR) for both the traditional DB plan and the innovative hybrid pension plan. Drawing on data from 90 employees at Company X, we assume an effective interest rate of 4% for the DB plan and explore various scenarios for the hybrid plan, ranging from 3% to 5%. The findings present a compelling narrative: the costs required to fund the hybrid plan are found to be notably lower than those for the DB plan, ushering in a more economically sustainable approach. Concurrently, the RR derived from the hybrid plan surpasses that of the DB plan, showcasing its potential to provide a more substantial post-retirement income. Additionally, as the effective interest rate escalates, costs rise, and RR declines, emphasizing the sensitivity of these parameters to the interest rate. Considering these results, a conclusion emerges: the hybrid pension plan stands out as the optimal choice for employees at Company X, presenting a novel and advantageous approach to pension program design and implementation.Keywords: Cost of pension benefits; Defined-benefit; Hybrid; Pension plan; Replacement ratio. AbstrakDalam penelitian ini, kami mendalami program pensiun, yang penting untuk menjamin penghidupan yang kuat setelah pensiun melalui pemberian manfaat pensiun kepada karyawan yang pensiun. Untuk mengatasi keseimbangan rumit antara keberlanjutan finansial dan mitigasi risiko, perusahaan diwajibkan mengalokasikan dana untuk manfaat pensiun. Program pensiun hybrid, yang merupakan penggabungan fitur manfaat pasti (DB) dan iuran pasti (DC), muncul sebagai solusi strategis untuk meminimalkan risiko yang melekat pada kedua model tersebut. Studi ini menghitung biaya yang terkait dengan manfaat pensiun dan replacement ratio (RR) untuk program DB dan program pensiun hybrid. Berdasarkan data dari 90 karyawan di Perusahaan X, kami mengasumsikan tingkat bunga efektif sebesar 4% untuk program DB dan menggunakan rentang 3% hingga 5% untuk program hybrid. Hasil penelitian menemukan bahwa biaya yang diperlukan untuk mendanai program hybrid ternyata jauh lebih rendah dibandingkan dengan program DB, sehingga menghasilkan pendekatan yang lebih berkelanjutan secara ekonomi. Pada saat yang sama, RR yang diperoleh dari program hybrid melampaui program DB, sehingga menunjukkan potensinya dalam memberikan pendapatan pasca-pensiun yang lebih besar. Selain itu, ketika tingkat bunga efektif meningkat, biaya meningkat, dan RR menurun. Hal ini menekankan sensitivitas parameter-parameter ini terhadap tingkat bunga efektif. Kesimpulannya program pensiun hybrid merupakan pilihan optimal bagi karyawan di Perusahaan X, karena menghadirkan pendekatan baru dan menguntungkan dalam perancangan dan implementasi program pensiun.Kata Kunci: Biaya manfaat pensiun; Dana pensiun; Defined-benefit; Hybrid; Replacement ratio. 2020MSC: 62P05. 
PERBANDINGAN KINERJA MODEL FTS-MARKOV CHAIN DAN GEOMETRIC BROWNIAN MOTION DALAM MEMPREDIKSI HARGA SAHAM BBRI Syifa Aulia; I Wayan Mangku; I Gusti Putu Purnaba
MILANG Journal of Mathematics and Its Applications Vol. 21 No. 2 (2025): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.21.2.163-177

Abstract

Saham merupakan bentuk investasi di pasar modal yang mampu menarik perhatian investor. Harga saham bersifat fluktuatif sehingga terjadi peningkatan dan penurunan harga. Model stokastik yang seringkali digunakan untuk memprediksi harga saham yaitu FTS-Markov Chain dan Geometric Brownian Motion (GBM). Penelitian ini bertujuan membandingkan kinerja dari model FTS-Markov Chain dan GBM dalam memprediksi harga saham. Kinerja kedua model prediksi dievaluasi dengan cara membandingkan nilai MAPE. Data yang digunakan adalah data harian harga penutupan saham BBRI sejak 01 November 2023 hingga 31 Oktober 2024 sebanyak 239 data. Data penelitian terbagi atas data training dan testing dengan proporsi masing-masing sebesar 80:20. Berdasarkan hasil penelitian, nilai MAPE yang diperoleh berdasarkan model FTS-Markov Chain dan GBM secara berturut-turut yaitu 1,19% dan 7,53%. Model FTS-Markov Chain menghasilkan nilai MAPE yang lebih kecil, sehingga dapat dikatakan bahwa hasil prediksi menggunakan FTS-Markov Chain lebih akurat dibandingkan GBM. Secara keseluruhan model FTS-Markov Chain mampu menangkap pola prediksi dan fluktuasi harga saham. Oleh sebab itu, model yang memiliki kinerja lebih baik dalam memprediksi harga saham BBRI adalah FTS-Markov Chain. Kata kunci: fuzzy time series Markov chain, harga saham, model GBM, prediksi
Analysis of Drought Characteristics in West Java Based on Return Period of Consecutive Dry Days Nabila, Amanda; Nurdiati, Sri; Purnaba, I Gusti Putu; Najib, Mohammad Khoirun
Jambura Geoscience Review Vol 8, No 1 (2026): Jambura Geoscience Review (JGEOSREV)
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jgeosrev.v8i1.32484

Abstract

Drought is one of the climate change phenomena that must be faced every year in some regions in Indonesia. West Java is a region that often experiences drought in Indonesia. Prolonged droughts are routinely experienced in some areas of West Java, while shorter periods of drought occur between rainfall events in several other regions of West Java. The characteristics of drought in West Java can be analyzed using one of the climate indicators, Consecutive Dry Days (CDD), based on the calculation of the return period of the climate indicator. Therefore, this study aims to analyze the characteristics of drought in West Java based on the calculation of the return period of the parametric distribution function by the CDD. Graph comparison and the Anderson-Darling test were used to estimate the parametric distribution function. Hourly ERA5-Land precipitation (1981–2022) was aggregated to daily totals; annual CDD was defined as the longest run of days with rainfall 1 mm, and return periods were computed using cut-off levels at the 75%, 85%, and 95% quantiles of the regional CDD distribution to map recurrence potential across cities and regencies. Based on the study's results, most of the CDD data in the West Java region have the fittest parametric distribution, namely the inverse Gaussian distribution, followed by the generalized extreme values, Weibull, and lognormal distributions. Further return period analysis shows that the area with the shortest return period to drought so that extreme drought often occurs, is the Indramayu Regency area. In that case, the areas with the longest drought return period are Bogor Regency, Bogor City, and Tasikmalaya City. These findings provide a distribution-based quantification of spatial drought recurrence in West Java to support early-warning and water-resources planning.
Co-Authors A. D. GARNADI Adilla, Indrya Amiruddin Saleh Amri Jahi Amri Jahi Amri Jahi Auliya Fithry Aunuddin . Awatif Berlian Setiawaty D. C. LESMANA D. S. Rahmawati Daniel Happy Putra Dara Irsalina Darwis S Gani Darwis S. Gani Darwis S. Gani Darwis S. Gani Dian Puspita Dian Puspita Djoko Susanto Djoko Susanto Donny Citra Lesmana Dwi Fidiana E. H. NUGRAHANI Erliana, Windiani Fendy Septyanto Fikri, Miftahul Fikriyah, Laila Qudrah Furlo Gilbert Godfrey Habel, Ine Febrianti Hadi Sumarno I Gede Setiawan Adi Putra I W. MANGKU I W. MANGKU I Wayan Mangku I. MAULIDI I. WIDIYASTUTI Indahwati Indrya Adilla Intansari, Kumala Iwan Tjitradjaja Iwan Tjitradjaja Iwan Tjitradjaja J. S. SELEKY Kelvin Gunawan Khairiati, Alfi Laila Qudrah Fikriyah Luky Adrianto M. FIKRI Ma'mun Sarma Maharani, Ardella Manjaruni, Vivin Aprilia Mokhamad O Royani Muh Hatta Jamil Muhammad Yusuf Sulaiman Nabila, Amanda Nahrul Hayati Najib, Mohammad Khoirun Nur Agustiani Pang S. Asngari Pang S. Asngari Prihandoko . Prihandoko Prihandoko Prihandoko S Prihandoko S Purwoko, Agus R. BUDIARTI Rafika Septiany Rahmah, Salsabilla Rahmawati, D. S. Retno Budiarti Rizki, Kurniadi Ruhiyat Ruhiyat Ruhiyat Ruhiyat Ruhiyat, Ruhiyat S. ARTIKA S. NURDIATI S. UTAMI Sapar . Sapar Sapar Septiany, Rafika Setyawan, Binar Aulia Sri Nurdiati Sugiyanta Sugiyanta Sulaiman, Muhammad Yusuf Syifa Aulia Tri Andika Julia Putra Vivin Manjaruni W. ERLIANA Windiani Erliana Windiani Erliana Windiani Erliana Y. ARBI Yolwi Dyatma Yolwi Dyatma Yuda Ardiansyah Yuda Ardiansyah Yudasril Yudasril _ Aunuddin