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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 InPrime: Indonesian Journal Of Pure And Applied Mathematics Jurnal Statistika dan Matematika (Statmat) Jurnal Statistika dan Aplikasinya Jurnal Pusat Inovasi Masyarakat 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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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. 
Pengaruh Inflasi terhadap Strategi Optimal Investasi dan Konsumsi dengan Model Stokastik Dara Irsalina; Retno Budiarti; I Gusti Putu Purnaba
Limits: Journal of Mathematics and Its Applications Vol. 19 No. 1 (2022): Limits: Journal of Mathematics and Its Applications Volume 19 Nomor 1 Edisi Me
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

The aim of this study is to investigate an optimal investment-consumption strategy under inflation rate with interest rate is described by Cox-Ingersol-Ross (CIR) model and volatility of the stock price is defined by Heston’s volatility model. A dynamic programming principle is used to obtain a Hamilton Jacobi Bellman (HJB) equation for the value function and choose a power utility function as utility function. The explicit solution of optimal investment and consumption are acquired with using separate variable and approach variable technique. The parameter’s values are approached by Euler-Maruyama method and Ordinary Least Square (OLS) method. Assumed that the portfolio of the investor contains a risk-free asset and a risk asset. Monthly historical data of TLK stock is used as risk asset and monthly historical data of BI 7-Day (Reverse) Repo Rate (BI7DRR) is used as risk-free asset, we obtain that the proportion of investment in stock is directly proportional to return of stock and the inflation rate does not have an impact on proportion investment in the stock. Meanwhile the optimal consumption of wealth is directly proportional to investor’s wealth and inversely proportional with inflation rate, which is the investor should consume less money of his wealth when the inflation rate increases.
Risk Analysis of Shallot Farm Income Using D-vine Copula-Based Monte Carlo Simulation Fatimah Fuzzaroh; Berlian Setiawaty; I Gusti Putu Purnaba
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41556

Abstract

Shallot farm income is highly uncertain due to fluctuations in yields, prices, and production costs, which are interdependent and significantly correlated. This study evaluates income risk by modeling the dependence structure among the variables that constitute income, while addressing data limitations. Two approaches are employed. First, a parametric approach models income as a univariate variable under the assumption of a normal distribution, ignoring dependence among its components. Second, a multivariate simulation approach utilizes a D-vine copula, combined with Monte Carlo simulation, to capture the dependence among income components and generate synthetic observations that better represent tail behavior. Risk is measured using Value-at-Risk (VaR) and Expected Shortfall (ES) based on 32 observations of average shallot farm income per harvest season over the period 2014–2024, and the results are compared with empirical estimates. Due to limited data, the empirical approach produces relatively coarse estimates, particularly in the tail region. The normal distribution approach yields higher and smoother estimates, indicating a higher level of risk. In contrast, the D-vine copula approach provides lower estimates than the normal distribution. These differences indicate that each method offers a distinct perspective on income risk.
Dependency of The Exchange Rate with The Volume of Indonesian Aluminum Exports Using Copula Kurniadi Rizki; Retno Budiarti; I Gusti Putu Purnaba
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.32517

Abstract

The downstreaming of bauxite, which is one of the raw materials for aluminum, indicates that the Indonesian government is serious about managing these mining resources. As one of the leading commodities, aluminum export activities not only affect investment but also strengthen the IDR-USD exchange rate. The increasing circulation of the rupiah has a positive impact on Indonesia in the international trade market. This study models the dependence between the IDR-USD exchange rate and Indonesia's aluminum export volume using copula. Copula doesn’t require the assumption of data normality, so it is very good for measuring the dependence of economic data that is often not normally distributed. The results of the study concluded that there is a positive correlation between the two variables, although it is not significant and is very small. This positive correlation indicates that the rupiah will strengthen along with the increasing volume of Indonesia's aluminum exports.
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 Epa Malasari Erliana, Windiani Fatimah Fuzzaroh Fendy Septyanto Fikri, Miftahul Fikriyah, Laila Qudrah Furlo Gilbert Godfrey Hadi Sumarno Hantrisa Nurrizki I Gede Setiawan Adi Putra I W. MANGKU I W. MANGKU I Wayan Mangku I. MAULIDI I. WIDIYASTUTI Indahwati Indrya Adilla Ine Febrianti Habel Intansari, Kumala Iwan Tjitradjaja Iwan Tjitradjaja Iwan Tjitradjaja J. S. SELEKY Kelvin Gunawan Khairiati, Alfi Kurniadi Rizki Laila Qudrah Fikriyah Luky Adrianto M. FIKRI Ma'mun Sarma Maharani, Ardella Manjaruni, Vivin Aprilia Mokhamad O Royani Muh Hatta Jamil Muhamad Ilham Zakaria Muhammad Akbar Zidane Muhammad Yusuf Sulaiman Nabilla Azah Azzara Nahrul Hayati Nur Agustiani Pang S. Asngari Pang S. Asngari Prihandoko . Prihandoko Prihandoko Prihandoko S Prihandoko S Purwoko, Agus R. BUDIARTI Radinda Swasti Maharani Rafika Septiany Rahma Nur Aini Azzahra 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 Siti Puji Rahayu Sugiyanta Sugiyanta Sulaiman, Muhammad Yusuf 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