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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) Limits: Journal of Mathematics and Its Applications Jambura Journal of Mathematics 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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PERAMALAN NILAI TUKAR RUPIAH TERHADAP DOLAR SINGAPURA, BAHT, DAN PESO MENGGUNAKAN METODE GSTAR Retno Budiarti; D. S. Rahmawati; Fendy Septyanto; I Gusti Putu Purnaba
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, 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 Retno Budiarti; Muhammad Yusuf Sulaiman; I Gusti Putu Purnaba; Windiani Erliana; Berlian Setiawaty; Ruhiyat
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, 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.
Determination of Term Life Insurance Premiums with Varying Interest Rates Following The CIR Model and Varying Benefits Value Puspita, Dian; Purnaba, I Gusti Putu; Lesmana, Donny Citra
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (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.v7i4.20542

Abstract

Term life insurance is an insurance that provides protection for a certain period that has been agreed upon in the policy. The policy is an agreement that contains the participant's obligation to pay premiums contributions to the insurance company and the insurance company's obligation to pay benefits in the event of a risk to the insurance participant as agreed in the policy. Interest rates will influence the calculation of premium value and benefits in the long term. So we need a model of interest rates that will change by time. One of the models that can be used is the CIR model. This research purposes to simulate the CIR model that will be carried out to determine interest rates for calculating term life insurance premiums for five years, with premiums paid at the beginning of the 1/m interval or monthly premium payments and benefits paid at the end of the 1/m interval when the participant dies. The case that will be discussed is when the benefit various. The results of this study are the CIR model can be applied to calculate the term life insurance premiums for five years and the premium calculation results show that the amount of the premium increase every year with varying benefits.
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. 
Portfolio Optimization for Rupiah Exchange Rate using Multidimensional Geometric Brownian Motion Model Masitah, Siti; Budiarti, Retno; Purnaba, I Gusti Putu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.29953

Abstract

Exchange rate fluctuations are critical in ensuring economic stability and shaping foreign investment, while foreign currencies serve as asset and wealth diversification instruments. This study aims to predict foreign exchange rates with a multidimensional geometric Brownian motion model and determine the optimal portfolio fund allocation with the Markowitz model using the Moore-Pendrose method. The multidimensional GBM model was employed for its ability to capture the volatility and interdependence among multiple currencies, making it more suitable for multi-asset portfolios than univariate models. The Markowitz model was used to determine the optimal asset allocation that achieves a specified expected return with minimal risk, while the Moore-Penrose method was applied to address matrix inversion challenges in high-dimensional data. Using data from 2023 to April 2024 on the Indonesian rupiah against the Singapore Dollar (SGD), Chinese Yuan (CNY), and Euro (EUR), this study finds that the multidimensional GBM model effectively forecasts exchange rate movements, as indicated by MAPE values below 10% for each currency. "The optimal portfolio yields a risk of 0.28% and an expected return of 0.009%, with asset allocations of 90.3% in SGD, 8.2% in CNY, and 1.5% in EUR. The dominance of SGD in the optimal portfolio suggests it was the most favorable investment option against the rupiah during the study period. This reflects Singapore's strong economic fundamentals and strategic position as a global financial hub. These findings provide valuable insights for investors and financial analysts seeking to manage currency risk and enhance returns through data-driven diversification strategies.
Dependency of The Exchange Rate with The Volume of Indonesian Aluminum Exports Using Copula Rizki, Kurniadi; Budiarti, Retno; Purnaba, I Gusti Putu
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): 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/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.
The Use of Monte Carlo Method to Model the Aggregate Loss Distribution Septiany, Rafika; Setiawaty, Berlian; Purnaba, I Gusti Putu
Al-Jabar: Jurnal Pendidikan Matematika Vol 11 No 1 (2020): Al-Jabar: Jurnal Pendidikan Matematika
Publisher : Universitas Islam Raden Intan Lampung, INDONESIA

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/ajpm.v11i1.6599

Abstract

Based on Law Number 24 of 2011, a state program was established to provide social protection and welfare for everyone, one of which is health insurance by the Social Insurance Administration Organization (BPJS). In its implementation, several important evaluations are needed. One that requires accurate evaluation is claim frequency and claim severity in determining premiums and reserved funds. This thesis provides one form of a method for selecting the distribution of claim frequency and claim severity. The data used in this study was taken from BPJS Health in the City of Tangerang in 2017. The distribution of opportunities chosen had been adjusted to the participant's claim data and parameter estimated using the Maximum Likelihood Estimation method. The chi-square test was used to check the goodness of fit for claim frequency distributions whereas the Anderson Darling tests were applied to claim severity distributions. The results of the chi-square test and the Anderson-Darling test showed that the model that matched the claim frequency distribution was the Z12M–NBGE distribution while the model that matched the claim severity was lognormal. The Z12M–NBGE distribution and the lognormal formed the aggregate loss distribution using the Monte Carlo method. Furthermore, the simulation results were obtained to the measurement of the Value in Risk (VaR) and Shortfall Expectations (ES). So, the Monte Carlo method is simple to implement the aggregate loss distributions and can easily handle various risks with dependency.  
Dependency Model of the Exchange Rate with the Volume Export of Mining Products in Indonesia Using Copula Rizki, Kurniadi; Budiarti, Retno; Purnaba, I Gusti Putu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.23089

Abstract

This research aims to analyze the dependence of the IDR-USD exchange rate on the volume of mining exports in Indonesia using the copula approach. This dependence is important to understand considering that the exchange rate and mineral exports have a direct impact on the country's economy which depends on foreign exchange from this sector. Mineral exports are one of the country's main sources of foreign exchange, while the exchange rate influences the competitiveness of exports on the international market. The mining products taken are iron and steel, copper and nickel, which are Indonesia's leading commodities. The copula method was chosen because of its ability to capture and model non-linear dependencies between variables, without considering the distribution of each variable. Copula makes it possible to model the marginal distribution of exchange rates and export volumes separately from their dependency structures, which is in line with the complex and dynamic nature of the Indonesian mining sector economy. The results show that there is no significant dependence between the exchange rate and the volume of commodity exports taken. Therefore, this commodity export volume policy will not have a significant effect on fluctuations in the IDR-USD exchange rate and vice versa. This article can be a recommendation for exporters to understand that export volumes do not need to pay attention to exchange rate fluctuations. 
THE COVID-19 PANDEMIC EFFECT ON THE DETERMINING CHILLI CROP AGRICULTURAL INSURANCE PREMIUM Manjaruni, Vivin Aprilia; Purnaba, I Gusti Putu; Budiarti, Retno
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 4 (2022): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (578.748 KB) | DOI: 10.30598/barekengvol16iss4pp1527-1540

Abstract

Parametric insurance is a type of insurance that contains an agreement related to triggering events between the insurer and the insured determined at the beginning of the contract. The provision that applies if the triggering event occurs is that the insurer (insurance company) is obliged to pay a sum of money (compensation) to the insured. Insurance based on area yield insurance is parametric insurance. Ozaki formulated an agricultural insurance model based on yields in an area called the parametric method. The loss of this method is a probability for crop loss that is in the area under the density function curve when the yield is smaller than the maximum guaranteed yield, but the losses calculated in this method only include losses due to crop failure and do not include losses due to the COVID-19 pandemic. Meanwhile, Susilowati and Gunawan, in their journals, explained that the production level of agricultural products, especially chili crops, during the COVID-19 pandemic, tended to be stable but not with the demand and purchasing power of the people, which significantly decreased. The significant decline in sales made farmers experience huge losses. Considering the COVID-19 pandemic impact, we were interested in formulating yield-based agricultural insurance models of chili crop that calculates the COVID-19 pandemic risk. So, the premiums rates and premiums obtained are more realistic and can reduce the risk of losses due to the COVID-19 pandemic for farmers, private companies, and the government.
THE APPLICATION OF DISCRETE HIDDEN MARKOV MODEL ON CROSSES OF DIPLOID PLANT Hayati, Nahrul; Setiawaty, Berlian; Purnaba, I Gusti Putu
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 3 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss3pp1449-1462

Abstract

The hidden Markov model consists of a pair of an unobserved Markov chain {Xk} and an observation process {Yk}. In this research, the crosses of diploid plant apply the model. The Markov chain {Xk} represents genetic structure, which is genotype of the kth generation of an organism. The observation process represents the appearance or the observed trait, which is the phenotype of the generation of an organism. Since it is unlikely to observe the genetic structure directly, the Hidden Markov model can be used to model pairs of events and unobservable their causes. Forming the model requires the use of the theory of heredity from Mendel. This model can be used to explain the characteristic of true breeding on crosses of diploid plants. The more traits crossed, the smaller probability of plants having a dominant phenotype in that period. Monohybrid, dihybrid, and trihybrid crosses have a dominant phenotype probability of 99% in the seventh, eighth, and ninth generations, with the condition of previous generations having a dominant phenotype. But in seventh generation, monohybrid crosses only have the probability of an optimal genotype of 50%, dihybrid crosses have a probability of an optimal genotype of 25% in the eighth generation, and trihybrid crosses have a probability of an optimal genotype of 12.5% in the ninth generation
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 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 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 Nahrul Hayati 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 Retno Budiarti Rizki, Kurniadi Ruhiyat Ruhiyat Ruhiyat Ruhiyat Ruhiyat, Ruhiyat S. ARTIKA S. NURDIATI S. UTAMI Sapar . Sapar Sapar Septiany, Rafika Setyawan, Binar Aulia 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 Yudasril _ Aunuddin