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All Journal Al-Jabar : Jurnal Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Zero : Jurnal Sains, Matematika, dan Terapan Jambura Journal of Mathematics Jurnal Matematika UNAND InPrime: Indonesian Journal Of Pure And Applied Mathematics Jurnal Statistika dan Matematika (Statmat) Milang Journal of Mathematics and Its Applications MILANG Journal of Mathematics and Its Applications
Berlian Setiawaty
School Of Data Science, Mathematics, And Informatics, IPB University, Bogor, Indonesia
Agriculture, Biological Sciences & Forestry Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Transportation Other

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Point and Figure Portfolio Optimization using Hidden Markov Models and Its Application on the Bumi Resources Tbk Shares Kastolan, Kastolan; Setiawaty, Berlian; Ardana, N. K. Kutha
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 3 No. 1 (2021)
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.v3i1.19376

Abstract

AbstractThe problem of portfolio optimization is to select a trading strategy which maximizes the expected terminal wealth. Since the stocks are traded at discrete random times in a real-world market, we are interested in a time sampling method. The sampling of stock price is obtained from the process of time sampling which is used in a point and figure chart. Point and figure (PF) chart displays the up and down movements of unbalanced stock prices. The basic idea is to describe essential movements of the unbalanced stock prices using a hidden Markov model. The model parameters are transition probability matrices. They are estimated using maximum likelihood method and expectation maximization algorithm. The estimation procedure involves change of measure. The model is then applied to the stock price of Bumi Resources Tbk. collected on a daily basis. The estimated parameters are used to calculate the optimal portfolio using a recursive algorithm. The results show that the discrete hidden Markov model can be applied to describe essential movements of the stock price. The best result gives 93.63% accuracy of the estimate of observation sequence with mean absolute percentage error (MAPE) 3.63%. The numerical calculation shows that the optimal logarithmic PF-portfolio increases the wealth.Keywords: point and figure portfolio; optimization portfolio; discrete hidden Markov model; expectation maximization algorithm; stock price of Bumi Resources Tbk. AbstrakMasalah pengoptimalan portofolio adalah pemilihan strategi perdagangan yang dapat memaksimalkan kekayaan terminal yang diharapkan. Karena di pasar dunia nyata, saham diperdagangkan pada waktu acak yang berbeda, sehingga kami tertarik pada metode pengambilan sampel waktu. Proses pengambilan sampel waktu diperoleh sampling harga saham yang digunakan dalam diagram point and figure (PF-chart). Grafik point and figure hanya menampilkan pergerakan naik atau turun harga saham yang tidak seimbang. Ide dasarnya adalah untuk mendeskripsikan pergerakan esensial dari harga saham yang tidak seimbang menggunakan model hidden Markov. Parameter dari model ini adalah matriks probabilitas transisi. Parameter diestimasi menggunakan metode maximum likelihood dan algoritma expectation maximization. Prosedur estimasi melibatkan perubahan ukuran. Model ini kemudian diaplikasikan pada harga saham Bumi Resources Tbk. dari tanggal 2 Januari 2007 sampai dengan 31 Januari 2011. Hasil estimasi parameter tersebut digunakan untuk menghitung portofolio optimal menggunakan algoritma rekursif. Hasil penelitian ini menunjukkan bahwa model hidden Markov diskrit dapat diterapkan untuk menggambarkan pergerakan esensial dari harga saham. Model terbaik memberikan akurasi 93.63% dari estimasi deretan observasi dengan mean absolute percentage error (MAPE) 3,63% dan 5 faktor penyebab kejadian. Perhitungan numerik menunjukkan bahwa logaritma portofolio-PF yang optimal dapat meningkatkan kekayaan.Kata kunci: portofolio point and figure; optimalisasi portofolio; model hidden Markov diskrit; algoritma expectation maximization; harga saham PT Bumi Resources.
LOSS INSURANCE MODEL OF RISK FOR AGRICULTURAL COMMODITY BASED ON MAXIMUM DAILY RAINFALL INDEX CONSIDERATION Muna, Siti Umamah Naili; Putu Purnaba, I Gusti; Setiawaty, Berlian
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0167-0178

Abstract

Agricultural commodities in rainfed areas face significant risks of yield loss and crop failure due to uncertain rainfall patterns and intensities. Index-based crop insurance has been introduced as an adaptive strategy to simplify loss assessment using climate indicators. However, most existing schemes cover only a single peril, such as drought. This study aims to develop a loss model of risk for agricultural commodity using maximum daily rainfall index that accounts for both drought and flood risks. The model consists of two components: rainfall modelling and insurance modelling. Rainfall modelling identifies the appropriate probability distribution to define rainfall index parameters—trigger and exit—which represent thresholds for yield reduction and total crop failure, respectively. These parameters are derived through numerical integration and can be approximated using percentiles when crop-specific water requirement data are unavailable. Insurance modelling determines a benefit claim model based on rainfall probability and parameters of rainfall index, with three possible benefit claim conditions: full, partial, and none. A case study using maximum daily rainfall data (September–December, 1984–2014) for paddy in Dramaga, Bogor, indicates that the Burr Type XII distribution fits the data better than the GEV distribution. The estimated premium ranges from IDR 300000 to 300822.9 per hectare. In high-rainfall areas like Dramaga, premiums are primarily influenced by the probability of excess rainfall, while drought risk is negligible. Analysis over a 10-year actual maximum daily rainfall data (September–December, 2015–2024) shows that lower insured percentiles result in lower premiums. To improve accuracy, trigger and exit should ideally be determined based on the specific crop's water requirements. Despite data limitations, this model provides a conceptual model for developing more representative and actuarially fair loss model for agricultural commodity risk.
Rainfall Risk Modelling for Rice Farming Using Continuous Hidden Markov Models Martal, David Vijanarco; Setiawaty, Berlian; Budiarti, Retno
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i3.25443

Abstract

Climate change has increased rainfall variability and unpredictability, significantly impacted agricultural productivity, and raised the risk of crop failure, particularly in rain-fed rice farming systems. This study models rainfall data from Tabanan, Bali, using a continuous-time Hidden Markov Model (HMM) to identify latent weather states and assess the associated risk of rice crop failure. The model assumes four hidden states, each generating rainfall observations following a Gamma distribution. Simulation results produced Mean Absolute Percentage Error (MAPE) values below 5% for training and testing sets, indicating strong model performance in replicating rainfall patterns. Risk analysis compared simulated rainfall with rice crop water requirements across three planting periods. The second planting period (July-October) exhibited the highest risk at 3.75%. Compared to other predictive models, HMM offers superior capability in capturing temporal rainfall structure and identifying critical transition phases, making it highly suitable for agricultural risk assessment and climate-adaptive planning.
ESTIMASI VALUE AT RISK DAN TAIL VALUE AT RISK SAHAM AGRO MENGGUNAKAN METODE PEAK OVER THRESHOLD DENGAN GENERALIZED PARETO DISTRIBUTION Setiawaty, Berlian; Hendartriany, Rayna Nurrizky; Muslimah, Hanifah; Hakim, Adhan Haidar; Aldena, Maulana Tata
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.21.2.75-88

Abstract

Investasi di pasar modal, khususnya pada saham dengan volatilitas tinggi seperti PT Bank Rakyat Indonesia Agroniaga Tbk (AGRO), mengandung risiko ketidakpastian yang signifikan. Asumsi distribusi normal seringkali gagal menangkap perilaku ekstrem pada data log-return saham yang memiliki karakteristik ekor berat. Penelitian ini bertujuan untuk mengukur risiko ekstrem menggunakan pendekatan Extreme Value Theory melalui metode Peak Over Threshold yang dimodelkan dengan Generalized Pareto Distribution. Data yang digunakan adalah log-return  harian saham AGRO periode Oktober 2022 hingga Oktober 2025. Analisis dilakukan secara terpisah pada ekor kiri untuk risiko kerugian dan ekor kanan untuk potensi keuntungan. Hasil estimasi menunjukkan adanya asimetri struktur ekor, di mana ekor kiri teridentifikasi memiliki batas yang pasti (ekor pendek), sedangkan ekor kanan bersifat ekor berat. Perhitungan Value at Risk dan Tail Value at Risk pada berbagai tingkat kepercayaan mengonfirmasi bahwa potensi keuntungan ekstrem secara statistik lebih dominan dibandingkan risiko kerugian ekstrem. Temuan ini memberikan informasi krusial bagi investor dalam menyusun strategi manajemen risiko yang lebih akurat dan efektif dibandingkan menggunakan metode konvensional. Kata kunci: Extreme Value Theory, Generalized Pareto Distribution, Peak Over Threshold, Tail Value at Risk, Value at Risk.
Co-Authors A. K. CRENATA Adilla, Indrya Aldena, Maulana Tata Ardana, N. K. Kutha Budiarti, Retno D. A. MUNAWAR D. C. LESMANA D. H. SANTOSO D. N. SARI D. P. ANGGRAINI Donny Citra Lesmana Erliana, Windiani F. BUKHARI Fendy Septyanto Fikri, Miftahul Fikriyah, Laila Qudrah Grifin Ryandi Egeten H. HIRASAWA Hakim, Adhan Haidar Hendartriany, Rayna Nurrizky I Gusti Putu Purnaba Indrya Adilla Istiadi, H. A. F. Kastolan Kastolan Kastolan, Kastolan L. KRISTINA Laila Qudrah Fikriyah M. FIKRI Maharani, Mutiara Martal, David Vijanarco Muhammad Taufik Abdillah Muhammad Yusuf Sulaiman Muna, Siti Umamah Naili Muslimah, Hanifah Muwafiqo Zamzami Dhuha N. K. K. ARDANA N. K. Kutha Ardana N. NURHASANAH Nahrul Hayati P. UTARI Putu Purnaba, I Gusti Rafika Septiany Retno Budiarti Ruhiyat Ruhiyat Ruhiyat Ruhiyat Ruhiyat, Ruhiyat S. A. PURNOMO S. F. NIKMAH Septiany, Rafika Sugi Guritman Sulaiman, Muhammad Yusuf Windiani Erliana Windiani Erliana Windiani Erliana Y. ADHARINI Yudasril Yudasril Yudasril Yudasril Yudasril, Yudasril