Article Per Year (5 Year)
p-Index From 2020 - 2025
5.268
P-Index
This Author published in this journals
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

Published : 52 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 3 Documents
Search
Journal : JTAM (Jurnal Teori dan Aplikasi Matematika)

 1 
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 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. 
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. 
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 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