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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society 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 Limits: Journal of Mathematics and Its Applications
Berlian Setiawaty
School Of Data Science, Mathematics And Informatics, IPB University
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.
Sifat Kemonotonan Barisan Trapezoid Sum dari Kelas Fungsi Nonkonveks dan Nonkonkaf Yudasril; Berlian Setiawaty; 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

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Abstract

The objective of this research is to show the monotonicity properties of the trapezoid sum sequence in general of nonconvex or nonconcave real valued continuous functions on interval corresponding to partitions of obtained by dividing into equal length subintervals. The decreasing monotony of the trapezoid sum generically does not happen in class of nonconcave functions. The same thing happens when restricted to the monotone nonconcave functions, namely in class of nonconcave increasing or nonconcave decreasing functions. Furthermore, in class of nonconvex functions, the trapezoid sum sequence generically does not increasing, as well as in class of increasing nonconvex or decreasing nonconvex functions.
Rainfall Risk Modelling for Rice Farming Using Continuous Hidden Markov Models David Vijanarco Martal; Berlian Setiawaty; Retno Budiarti
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.
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.
PERBANDINGAN ESTIMASI PREMI KLAIM ASURANSI KESEHATAN BERDASARKAN WILAYAH DAN STATUS PEROKOK MENGGUNAKAN MODEL BÜHLMANN–STRAUB Berlian Setiawaty; Annisa Aulia Putri; Bagus Handoko; Dendy Aditya; Monica Dewi Putri Kusmana; Ruhiyat
MILANG Journal of Mathematics and Its Applications Vol. 22 No. 1 (2026): 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.22.1.15-26

Abstract

Peningkatan klaim asuransi kesehatan menuntut perusahaan asuransi menetapkan premi yang lebih sesuai dengan tingkat risiko. Penelitian ini bertujuan untuk mengestimasi dan membandingkan premi kredibilitas murni pada portofolio asuransi kesehatan menggunakan model semiparametrik Bühlmann-Straub, dengan fokus pada kombinasi faktor risiko status perokok dan wilayah tempat tinggal. Data yang digunakan adalah data besar klaim asuransi kesehatan dari Kaggle tahun 2023 yang dikelompokkan menjadi empat kelompok berdasarkan status perokok, bukan perokok dan region yaitu Southeast dan Northeast. Data besar klaim keempat kelompok tersebut dimodelkan menggunakan sebaran lognormal dan Weibull. Hasil penelitian menunjukkan bahwa model kredibilitas Bühlmann–Straub efektif menghasilkan premi asuransi kesehatan yang lebih akurat pada portofolio heterogen, dengan status perokok terbukti menjadi faktor risiko paling dominan dibandingkan wilayah. Faktor kredibilitas (Z) yang dihasillkan sangat tinggi, berkisar pada 0,99, menandakan bahwa pengalaman klaim tiap kelompok dapat diandalkan dalam penentuan premi. Hasil estimasi premi akhir tertinggi diperoleh kelompok perokok di Southeast (34841,838), sedangkan yang terendah adalah bukan perokok di Southeast (8296,787).
ESTIMASI VALUE AT RISK DAN TAIL VALUE AT RISK SAHAM AGRO MENGGUNAKAN METODE PEAK OVER THRESHOLD DENGAN GENERALIZED PARETO DISTRIBUTION Berlian Setiawaty; Rayna Nurrizky Hendartriany; Hanifah Muslimah; Adhan Haidar Hakim; Maulana Tata Aldena
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.
LOSS INSURANCE MODEL OF RISK FOR AGRICULTURAL COMMODITY BASED ON MAXIMUM DAILY RAINFALL INDEX CONSIDERATION Siti Umamah Naili Muna; I Gusti Putu Purnaba; Berlian Setiawaty
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.
Modelling The US Dollar Index Using Continuous Hidden Markov David Vijanarco Martal; Berlian Setiawaty; Retno Budiarti
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.1986

Abstract

This study employs the continuous hidden Markov model (HMM) to model the index data of the US Dollar index from 2018 to 2024. HMM is used to predict and analyze hidden patterns that generated the data. The data is modelled using a continuous HMM with 11 hidden states and lognormal distributions with different parameters for each hidden state. The accuracy of the continuous HMM is measured by MAPE. The MAPE value for both training and testing data is very low, less than 4%. This means that the continuous HMM can be used to model the data accurately. The plot shows accurate predictions between simulated data and real data, and furthermore, the model can capture the fluctuations of the data.
Co-Authors A. K. CRENATA Adhan Haidar Hakim Adilla, Indrya Annisa Aulia Putri Ardana, N. K. Kutha Bagus Handoko D. A. MUNAWAR D. C. LESMANA D. H. SANTOSO D. N. SARI D. P. ANGGRAINI David Vijanarco Martal David Vijanarco Martal Dendy Aditya Donny Citra Lesmana Erliana, Windiani F. BUKHARI Fatimah Fuzzaroh Fendy Septyanto Fikri, Miftahul Fikriyah, Laila Qudrah Grifin Ryandi Egeten H. HIRASAWA Hanifah Muslimah I Gusti Putu Purnaba I Gusti Putu Purnaba I Gusti Putu Purnaba Indrya Adilla Istiadi, H. A. F. Kastolan Kastolan Kastolan, Kastolan L. KRISTINA Laila Qudrah Fikriyah M. FIKRI Maharani, Mutiara Maulana Tata Aldena Monica Dewi Putri Kusmana Muhammad Taufik Abdillah Muhammad Yusuf Sulaiman Muwafiqo Zamzami Dhuha N. K. K. ARDANA N. K. Kutha Ardana N. NURHASANAH Nahrul Hayati P. UTARI Rafika Septiany Rayna Nurrizky Hendartriany Retno Budiarti Retno Budiarti Retno Budiarti Ruhiyat Ruhiyat Ruhiyat Ruhiyat Ruhiyat, Ruhiyat S. A. PURNOMO S. F. NIKMAH Septiany, Rafika Siti Umamah Naili Muna Sugi Guritman Sulaiman, Muhammad Yusuf Windiani Erliana Windiani Erliana Windiani Erliana Y. ADHARINI Yudasril Yudasril Yudasril Yudasril Yudasril Yudasril, Yudasril