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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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The Solution of Generalization of the First and Second Kind of Abel’s Integral Equation Muhammad Taufik Abdillah; Berlian Setiawaty; Sugi Guritman
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.v7i3.14193

Abstract

Integral equations are equations in which the unknown function is found to be inside the integral sign. N. H. Abel used the integral equation to analyze the relationship between kinetic energy and potential energy in a falling object, expressed by two integral equations. This integral equation is called Abel's integral equation. Furthermore, these equations are developed to produce generalizations and further generalizations for each equation. This study aims to explain generalizations of the first and second kind of Abel’s integral equations, and to find solution for each equation. The method used to determine the solution of the equation is an analytical method, which includes Laplace transform, fractional calculus, and manipulation of equation. When the analytical approach cannot solve the equation, the solution will be determined by a numerical method, namely successive approximations. The results showed that the generalization of the first kind of Abel’s integral equation solution can be determined using the Laplace transform method, fractional calculus, and manipulation of equation. On the other hand, the generalization of the second kind of Abel’s integral equation solution is obtained from the Laplace transform method. Further generalization of the first kind of Abel’s integral equation solution can be obtained using manipulation of equation method. Further generalization of the second kind of Abel’s integral equation solution cannot be determined by analytical method, so a numerical method (successive approximations) is used. 
LOSS ELIMINATION RATIO OF TOTAL MOTOR VEHICLE INSURANCE LOSSES USING ORDINARY DEDUCTIBLE Setiawaty, Berlian; Maharani, Mutiara; Ruhiyat, Ruhiyat; Erliana, Windiani
Jurnal Matematika UNAND Vol 14, No 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.1-13.2025

Abstract

Penelitian ini membahas total kerugian dari asuransi kendaraan bermotor jika diterapkan ordinary deductible. Data yang digunakan dalam penelitian ini adalah data Motorcycle Insurance dari package insuranceData R. Pemodelan total kerugian dilakukan dengan memodelkan banyak klaim menggunakan sebaran binomial negatif dan besar klaim menggunakan sebaran beta-prime. Sebaran total kerugian merupakan sebaran compound dengan sebaran primernya binomial negatif dan sebaran sekundernya beta-prime. Sebaran compound ini sulit diperoleh bentuk analitiknya sehingga digunakan simulasi Monte Carlo. Dengan simulasi Monte Carlo dapat dihitung nilai harapan kerugian agregat tanpa ordinary deductible maupun dengan ordinary deductible, sehingga diperoleh loss elimination ratio dari penggunaan ordinary deductible. Dari perhitungan yang dilakukan dapat disimpulkan semakin besar nilai ordinary deductible, semakin meningkat pula loss elimination ratio-nya.
LOSS ELIMINATION RATIO OF TOTAL MOTOR VEHICLE INSURANCE LOSSES USING ORDINARY DEDUCTIBLE Setiawaty, Berlian; Maharani, Mutiara; Ruhiyat, Ruhiyat; Erliana, Windiani
Jurnal Matematika UNAND Vol. 14 No. 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.1-13.2025

Abstract

Penelitian ini membahas total kerugian dari asuransi kendaraan bermotor jika diterapkan ordinary deductible. Data yang digunakan dalam penelitian ini adalah data Motorcycle Insurance dari package insuranceData R. Pemodelan total kerugian dilakukan dengan memodelkan banyak klaim menggunakan sebaran binomial negatif dan besar klaim menggunakan sebaran beta-prime. Sebaran total kerugian merupakan sebaran compound dengan sebaran primernya binomial negatif dan sebaran sekundernya beta-prime. Sebaran compound ini sulit diperoleh bentuk analitiknya sehingga digunakan simulasi Monte Carlo. Dengan simulasi Monte Carlo dapat dihitung nilai harapan kerugian agregat tanpa ordinary deductible maupun dengan ordinary deductible, sehingga diperoleh loss elimination ratio dari penggunaan ordinary deductible. Dari perhitungan yang dilakukan dapat disimpulkan semakin besar nilai ordinary deductible, semakin meningkat pula loss elimination ratio-nya.
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.  
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
PENENTUAN PREMI TAHUNAN BERSIH ASURANSI JIWA SEUMUR HIDUP JOINT LIFE DENGAN MODEL COPULA CLAYTON DAN COPULA GUMBEL Fikriyah, Laila Qudrah; Purnaba, I Gusti Putu; Erliana, Windiani; Setiawaty, Berlian; Lesmana, Donny Citra
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 1 (2022): 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.18.1.15-28

Abstract

Asuransi jiwa seumur hidup adalah bentuk pengalihan risiko atas kerugian keuangan oleh tertanggung kepada penanggung yang disebabkan oleh hilangnya jiwa seseorang setelah polis disepakati. Pada status joint life pasangan suami istri Premi dibayarkan setiap tahun dan pembayaran manfaat dilakukan pada akhir tahun kematian pertama. Biasanya risiko kematian pasangan suami istri diasumsikan saling bebas, namun dalam kenyataannya kerap kali pasangan suami istri memiliki risiko bersama. Pada karya ilmiah ini, dilakukan penghitungan premi bersih tahunan dari asuransi jiwa seumur hidup joint life bagi pasangan suami istri menggunakan dua asumsi: (1) kebebasan mortalitas dan (2) ketidakbebasan mortalitas dengan model copula Clayton dan copula Gumbel. Berdasarkan hasil perhitungan untuk contoh kasus yang spesifik, premi tahunan yang dihitung menggunakan asumsi kebebasan mortalitas lebih besar jika dibandingkan dengan menggunakan asumsi ketidakbebasan mortalitas. Hasil ini berlaku juga untuk suku bunga yang bervariasi.
PREMI BERSIH TAHUNAN ASURANSI JIWA BERJANGKA UNTUK KASUS MULTIPLE DECREMENT DENGAN VARIASI SUKU BUNGA Adilla, Indrya; I Gusti Putu Purnaba; Ruhiyat; Berlian Setiawaty; Windiani Erliana; Septyanto, Fendy
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 2 (2022): 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.18.2.139-153

Abstract

Aplikasi penggunaan model multiple decrement terdapat pada asuransi jiwa dengan tambahan manfaat dan dana pensiun. Manfaat dibayarkan bergantung pada penyebab keluarnya peserta dari asuransi. Untuk menentukan besar premi dan nilai manfaat pada suatu waktu diperlukan data Tabel Penyusutan Jamak dan asumsi suku bunga. Penelitian ini bertujuan untuk mengkonstruksi Tabel Penyusutan Jamak dari data Illustrative Service Table yang tersedia di library software R dan menentukan besar premi bersih tahunan asuransi jiwa berjangka 35 tahun untuk seseorang yang berusia 30 tahun yang memberikan manfaat kematian, mengundurkan diri, cacat permanen, dan pensiun dengan variasi suku bunga. Menggunakan suku bunga konstan diperoleh besar premi bersih tahunan dari 3.5% sampai 15% akan menurun semakin bertambahnya suku bunga, namun kembali meningkat dari suku bunga 15% hingga 20%. Besar premi bersih tahunan dengan asumsi suku bunga bervariasi mengikuti besar suku bunga nominal Republik Korea (yang telah dimodifikasi) lebih kecil dibandingkan dengan premi ketika diasumsikan suku bunga konstan sebesar rata-rata suku bunga nominal tersebut.
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.
ESTIMASI TAIL VALUE AT RISK RETURN PORTOFOLIO TIGA OBLIGASI MENGGUNAKAN SIMULASI MONTE-CARLO Setiawaty, Berlian; Istiadi, H. A. F.; Ruhiyat; Erliana, Windiani
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 2 (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.20.2.77-87

Abstract

Tail Value at Risk (TVaR) adalah salah satu ukuran untuk menunjukkan tingkat risiko, salah satunya adalah risiko investasi pada obligasi. Penelitian ini bertujuan untuk mengestimasi TVaR return portofolio yang terdiri atas tiga obligasi, yaitu OBMR, OSSB, dan OBJB. Data yang digunakan adalah data harga obligasi harian OBMR, OSSB, dan OBJB dari tanggal 1 Oktober 2022 sampai 30 Desember 2022. Untuk menyusun portofolio yang optimal, digunakan metode Mean-Variance Efficient Portfolio. Proporsi portofolio optimal terdiri atas OBMR 82.28%, OSSB 3.99%, dan OBJB 13.73%. Menggunakan proporsi tersebut diperoleh return portofolio. Untuk menghitung TVaR return portofolio diperlukan sebaran setiap return obligasi. Dari hasil penghitungan, diperoleh return OBMR dan OBJB menyebar logistik, dan return OSSB menyebar normal. Menggunakan simulasi Monte-Carlo diperoleh estimasi sebaran return portofolio. Dari sebaran tersebut diperoleh estimasi TVaR return portofolio. Hasil penghitungan menunjukkan bahwa semakin besar tingkat kepercayaan yang digunakan, semakin besar pula risiko kerugian (TVaR). Semakin lama periode waktu pengukuran, semakin tinggi pula risikonya yang ditunjukkan oleh semakin tingginya nilai TVaR.
SIFAT KEMONOTONAN PADA JUMLAH TRAPESIUM DARI HAMPIRAN FUNGSI-FUNGSI KONVEKS Yudasril, Yudasril; Setiawaty, Berlian
STATMAT : JURNAL STATISTIKA DAN MATEMATIKA Vol 3 No 1 (2021)
Publisher : Math Program, Math and Science faculty, Pamulang University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32493/sm.v3i1.8340

Abstract

Selain jumlah Darboux, jumlah trapesium juga dapat digunakan dalam menghampiri luas daerah di bawah kurva dari suatu fungsi 𝑓 real taknegatif pada suatu interval [𝑎, 𝑏]. Untuk setiap partisi 𝑃𝑛 yang membagi interval [𝑎, 𝑏] menjadi 𝑛 subinterval dengan jarak yang sama, dibentuk suatu pendekatan dari nilai integral atau luas di bawah kurva 𝑓 pada [𝑎, 𝑏] yakni, jumlah trapesium 𝑇𝑛 (𝑓). Dalam tulisan ini, akan diperlihatkan bahwa terdapat suatu fungsi linear sesepenggal 𝑔 yang menghampiri fungsi konveks 𝑓 sedemikian sehingga ekor barisan dari barisan jumlah trapesium {𝑇𝑛 (𝑔)}𝑛=1 ∞ adalah monoton naik.
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