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All Journal JBIO: jurnal biosains (the journal of biosciences) CAUCHY: Jurnal Matematika Murni dan Aplikasi Althea Medical Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Journal of Epidemiology and Public Health Jambura Journal of Mathematics M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika GREENOMIKA Jurnal Kesehatan Jurnal Pendidikan Administrasi Perkantoran (JPAP) Milang Journal of Mathematics and Its Applications Jurnal Indonesia Sosial Sains Proceeding Applied Business and Engineering Conference MILANG Journal of Mathematics and Its Applications Limits: Journal of Mathematics and Its Applications
Retno Budiarti
Department Of Mathematics, Faculty Of Mathematics And Natural Sciences, Bogor Agricultural University, Jl. Meranti, Kampus IPB Darmaga, Bogor
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Price Model with Generalized Wiener Process for Life Insurance Company Portfolio Optimization using Mean Absolute Deviation Putra, Hilman Yusupi Dwi; Silalahi, Bib Paruhum; Budiarti, Retno
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.v8i4.23093

Abstract

The Financial Services Authority (OJK) has issued Regulation of the Financial Services Authority of the Republic of Indonesia Number 5 Year 2023. Article 11 paragraph 1d explains the limitations of assets allowed in the form of investment, investment in the form of shares listed on the stock exchange for each issuer is a maximum of 10% of the total investment and a maximum of 40% of the total investment. The investment manager of a life insurance company needs to adjust its investment portfolio. In 1991, Konno and Yamazaki proposed an approach to the portfolio selection problem with Mean Absolute Deviation (MAD) model. This model can be solved using linear programming, effectively solving high-dimensional portfolio optimization problems. Another problem in stock portfolio formation is that the ever-changing financial markets demand the development of models to understand and forecast stock price behavior. One method that has been widely used to model stock price movements is the generalized Wiener Process. The generalized Wiener process provides a framework that can accommodate the stochastic nature of stock price changes, thus allowing portfolio managers to be more sensitive to unanticipated market fluctuations. The stock price change model using the Generalized Wiener Process is very good at predicting stock price changes. The results of this stock price prediction can then be used to find the optimal portfolio using the MAD model. The portfolio optimization problem with the MAD model can be solved using linear programming to obtain the optimal stock portfolio for life insurance companies. 
IMPLEMENTATION OF MONTE CARLO MOMENT MATCHING METHOD FOR PRICING LOOKBACK FLOATING STRIKE OPTION Dewi, Komang Nonik Afsari; Lesmana, Donny Citra; 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 (444.026 KB) | DOI: 10.30598/barekengvol16iss4pp1365-1372

Abstract

Monte Carlo method was a numerical method that was popular in finance. This method had disadvantages at convergences, so the moment matching was used to improve the efficiency from Monte Carlo method. The research has discussed about pricing of the lookback floating strike option using the Monte Carlo moment matching method. The monthly stock price of PT TELKOM from 2004 to 2021 that used in this research. The results obtained by adding variance reduction moment matching in Monte Carlo method, which produces a relatively had smaller error when compared to the relative error of the standard Monte Carlo method. The orders of convergence from Monte Carlo method with variance reduction moment matching for call and put option are about 1.1 and 1.4. The conclusion that addition of the moment matching can increase the efficiency of the Monte Carlo method in determining the price of the lookback floating strike option.
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.
PRICING EUROPEAN BASKET OPTION USING THE STANDARD MONTE CARLO AND ANTITHETIC VARIATES Sitepu, Sanfriska Br; Lesmana, Donny Citra; Budiarti, Retno
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 2 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss2pp1007-1016

Abstract

DETERMINING THE VALUE OF DOUBLE BARRIER OPTION USING STANDARD MONTE CARLO, ANTITHETIC VARIATE, AND CONTROL VARIATE METHODS Silalahi, Romaito Br; Lesmana, Donny Citra; Budiarti, Retno
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 2 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss2pp1017-1026

Abstract

In this paper, we applied the standard Monte Carlo, antithetic variate, and control variates methods to value the double barrier knock-in option price. The underlying asset used in the calculation of double barrier knock-in option is the share of ANTM from April 1, 2019 until March 1, 2022. The value of the double barrier knock-in option is simulated using standard Monte Carlo, antithetic variate, and control variates methods. The results showed that all the methods converge to the exact solution, with the control variate method to be the fastest. Standard Monte Carlo method has the least computational time, followed by control variate and antithetic variate method. Compared to the other methods, control variate is the most effective and efficient in determining the value of double barrier knock-in option, based on the option value, relative error and computational time. Antithetic variate method converges faster to the exact solution compared to standard Monte Carlo. However it has the longest computation time compared to the other methods.
ANALYSIS OF THE DEPENDENCIES COMMODITY PRICES AND STOCK MARKET INDEXES USING COPULA Rahmah, Salsabilla; Budiarti, Retno; Purnaba, I Gusti Putu
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss3pp1563-1572

Abstract

Indonesia is rich in natural resources and occupies an important position in the global raw materials market. The country's rich resources such as oil, coal, nickel, and crude palm oil (CPO) have a significant impact on the economic situation. As one of the world's leading producers and exporters of these raw materials, Indonesia's economic fate is closely linked to price fluctuations. This study uses the copula method to model the dependence between stock and commodity returns and calculates the dependence between commodity prices (oil, coal, nickel, CPO) and Indonesian stock market index (IHSG) The data used for this analysis was sourced from Bloomberg.com, covering the period from 29 September 2021 to 29 September 2023. This study investigates the dynamic dependencies between commodity price returns and the Indonesian stock market index. The results show that the correlations between oil prices and the Indonesian stock index, and between CPO prices and the stock index are generally weak. However, there are exceptions to stock index returns, such as their relatively high dependence on coal and nickel. This diverse research provides valuable insight into the complex interdependencies in Indonesia's financial landscape. Understanding dependence between commodity prices and stock indexes is of great value to investors and policymakers, as it is the basis for making informed decisions to navigate the complex global economy.
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.
Confidence Interval for Variance Function of a Compound Periodic Poisson Process with a Power Function Trend Irawan, Ade; Mangku, I Wayan; Budiarti, Retno
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.v7i3.14836

Abstract

This research is a follow-up research of Utama (2022) on asymptotic distribution of an estimator for variance function of a compound periodic Poisson with the power function trend. The objectives of this research are (i) to formulate a confidence interval for the variance function of a compound periodic Poisson process with a power function trend and (ii) to prove the convergence to 1-α probability of the parameter included in the confidence interval. This research process begins with a review of the existing formulation of the variance function estimator and its asymptotic distribution. Next, the confidence interval for the variance function of the compound periodic Poisson process with a power function trend is formulated and the convergence to 1-α is determined. After obtaining the confidence interval, the research continued by conducting computer simulations to confirmed the results obtained analytically. The results obtained show that the confidence interval for the variance function of a compound periodic Poisson process with a power function trend converges to 1-α both analytically and numerically for different finite time intervals.
Co-Authors Ade Irawan Adriani, Ika Reskiana Aldinasyah, Monicha Zalzabilla Anang Kistyanto Andre Dwijanto Witjaksono Asri Rahmawati Berlian Setiawaty Bib Paruhum Silalahi Chalimatusadiah Chalimatusadiah D. S. Rahmawati Daniel Happy Putra Dara Irsalina Dewi, Komang Nonik Afsari Diana, Adawiyah Putri Donny Citra Lesmana Dwi Fidiana Endar Hasafah Nugrahani Erliana, Windiani Fendy Septyanto Garianto, Efyluk Grifin Ryandi Egeten Habel, Ine Febrianti Hadi Sumarno Helynda Mulya Arga Retha Helynda Mulya Arga Retha Hemarani, Febri Herdiyantini, Mita I Gusti Putu Purnaba I Wayan Mangku Intansari, Kumala Khairiati, Alfi Khairiati, Alfi Khan, Joan Lusiana Sani Parwati Manjaruni, Vivin Aprilia Mohammad Reza Muhammad Yusuf Sulaiman Mulyasari, Rindi Melati Najib, Mohamad Khoirun Nashiruddin, Muhammad Abdurrasyid Nefertiti, Eva Nur Agustiani Prasetya, Hanung Priambodo, Bima Putra, Hilman Yusupi Dwi Putra, Oki Nugraha Rafhida, Syukri Arif Rahadianto, Rahadianto Rahmah, Salsabilla Rahmawati, D. S. Rizki, Kurniadi Ronald Pratama Adiwinoto Ruhiyat Ruhiyat S. Soedarsono Setyawan, Binar Aulia Silalahi, Romaito Br siswadi - Sitepu, Sanfriska Br Sri Nurdiati Sudiarta, Ketut Edy Sulaiman, Muhammad Yusuf Titut Harnanik Utami, Nadila Rizqi Windiani Erliana Yulianty, Sherly