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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) Jambura Journal of Mathematics Jambura Geoscience Review 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

Author-ID : 284149

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

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PENENTUAN PREMI ASURANSI JIWA BERJANGKA MENGGUNAKAN MODEL VASICEK DAN MODEL COX-INGERSOLL-ROSS (CIR) S. ARTIKA; I. G. P. PURNABA; D. C. LESMANA
MILANG Journal of Mathematics and Its Applications Vol. 17 No. 2 (2018): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Tingkat suku bunga berpengaruh pada penentuan besaran nilai premi. Nilai suku bunga diperoleh dengan menggunakan model suku bunga Vasicek dan CIR. Tujuan dari penelitian ini adalah untuk menghitung nilai suku bunga, nilai premi, dan perbandingan nilai premi dari model suku bunga Vasicek dan model suku bunga CIR. Nilai suku bunga akan digunakan dalam menghitung nilai premi asuransi jiwa berjangka ???? tahun dengan pembayaran cicilan premi saat besaran konstan tapi berbeda untuk dua periode dan cicilan premi saat besaran meningkat secara linear ketika uang pertanggungan dibayarkan di akhir tahun. Hasil perhitungan premi asuransi jiwa berjangka dengan model Vasicek dan model CIR tidak ada perbedaan yang signifikan.

EVALUASI NUMERIK PENDUGA FUNGSI NILAI HARAPAN DAN FUNGSI RAGAM PROSES POISSON MAJEMUK DENGAN INTENSITAS EKSPONENSIAL FUNGSI LINEAR S. UTAMI; I W. MANGKU; I G. P. PURNABA
MILANG Journal of Mathematics and Its Applications Vol. 17 No. 2 (2018): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Performances of estimators for the mean and variance functions of a compound Poisson process having intensity obtained as an exponential of linear function are investigated using Monte Carlo simulations. The intensity function of this process is assumed to be ????????????(????+????????) with 0<????<∞, where ???? is assumed to be known. In [8], estimators of the mean and variance functions of this process have been constructed and have been proved to be unbiased, weakly and strongly consistent. The objectives of this research are to check distributions of these estimators using Monte Carlo simulation and to check the convergence to 1−???? of the probabilities that the parameters are contained in the confidence intervals constructed in [11]. Results of the research are as follows. Distribution of estimators for the mean and variance functions are approximately normal. For a given significance level ????, the larger the size of observation interval, the closer the probabilities that the parameters are contained in the confidence intervals to 1−????.

PENENTUAN PREMI TAHUNAN BERSIH ASURANSI JIWA SEUMUR HIDUP JOINT LIFE DENGAN MODEL COPULA CLAYTON DAN COPULA GUMBEL Laila Qudrah Fikriyah; I Gusti Putu Purnaba; Windiani Erliana; Berlian Setiawaty; Donny Citra Lesmana
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 1 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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 Indrya Adilla; I Gusti Putu Purnaba; Ruhiyat; Berlian Setiawaty; Windiani Erliana; Fendy Septyanto
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 2 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

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.

Penerapan Analisis Regresi Logistik Ordinal pada Asuransi Kredit Perdagangan Domestik Kelvin Gunawan; Ruhiyat; I Gusti Putu Purnaba
Jurnal Statistika dan Aplikasinya Vol 6 No 2 (2022): Jurnal Statistika dan Aplikasinya
Publisher : Program Studi Statistika FMIPA UNJ

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/JSA.06220

One of the main activities that support the national economy is domestic trade. However, domestic trade is faced with various risks. One risk is that the buyer fails to fulfil his obligation to pay. The seller can overcome this risk by purchasing a domestic trade credit insurance product from an insurance company. The premium rate must be calculated correctly so that the insurance company does not suffer losses. Premium rates can be grouped based on several factors. Ordinal logistic regression analysis can be used to group premium rates and identify factors that affect premium rate groups. The maximum likelihood method can be used to estimate the parameters of the ordinal logistic regression model. In this study, two logit models were produced, and the premium rate group was significantly affected by the payment tenor, central credit limit, and the type of commodity. Overall, the classification accuracy value generated from the ordinal logistic regression model that has been built is 57.45%.

Determination of Term Life Insurance Premiums with Varying Interest Rates Following The CIR Model and Varying Benefits Value Dian Puspita; I Gusti Putu Purnaba; Donny Citra Lesmana
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i4.20542

Term life insurance is an insurance that provides protection for a certain period that has been agreed upon in the policy. The policy is an agreement that contains the participant's obligation to pay premiums contributions to the insurance company and the insurance company's obligation to pay benefits in the event of a risk to the insurance participant as agreed in the policy. Interest rates will influence the calculation of premium value and benefits in the long term. So we need a model of interest rates that will change by time. One of the models that can be used is the CIR model. This research purposes to simulate the CIR model that will be carried out to determine interest rates for calculating term life insurance premiums for five years, with premiums paid at the beginning of the 1/m interval or monthly premium payments and benefits paid at the end of the 1/m interval when the participant dies. The case that will be discussed is when the benefit various. The results of this study are the CIR model can be applied to calculate the term life insurance premiums for five years and the premium calculation results show that the amount of the premium increase every year with varying benefits.

Cadangan Manfaat Minimum dan Maksimum Asuransi Jiwa Seumur Hidup dan Berjangka dengan Metode Prospektif Yolwi Dyatma; I Gusti Putu Purnaba; Hadi Sumarno
Jurnal Matematika Integratif Vol 18, No 1: April 2022
Publisher : Department of Matematics, Universitas Padjadjaran

Menentukan cadangan manfaat asuransi jiwa perlu dilakukan oleh perusahaan asuransi agar dapat membayarkan klaim nasabahnya dikemudian hari. Dengan menggunakan produk asuransi jiwa seumur hidup dan berjangka 40 tahun akan ditentukan nilai cadangan manfaat minimum dan maksimum dari suatu perusahaan asuransi. Mengambil penelitian untuk nasabah perempuan yang menggunakan produk perusahaan asuransi jiwa seumur hidup dengan tingkat suku bunga 6% didapatkan nilai cadangan manfaatnya setelah 25 tahun menggunakan asuransi jiwa seumur hidup sebesar Rp168.436.406,10. Dan untuk asuransi jiwa berjangka 40 tahun nilai cadangan manfaat setelah 20 tahun sebesar Rp241.081.101,40. Dari hasil yang diperoleh dapat digunakan oleh perusahaan asuransi dalam menentukan cadangan manfaat perusahaannya.

PENENTUAN PREMI DAN CADANGAN MANFAAT ASURANSI JIWA JOINT LIFE SAAT TINGKAT BUNGA DIMODELKAN DENGAN COX-INGERSOLL-ROSS Yuda Ardiansyah; Windiani Erliana; Ruhiyat; I Gusti Putu Purnaba; Fendy Septyanto
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 1 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.1.23-41

Pada karya ilmiah ini dibahas asuransi jiwa joint life untuk tiga orang tertanggung dengan tingkat bunga model Cox-Ingersoll-Ross (CIR). Manfaat dari asuransi jiwa tersebut dibayarkan setelah tahun kesepuluh jika tidak ada kematian terjadi, kematian pertama, atau kematian kedua pada peserta asuransi. Tingkat bunga yang digunakan dalam karya ilmiah ini adalah tingkat bunga BI 7-day (Reverse) Repo Rate (BI7DRR) periode September 2016 sampai September 2022 yang dimodelkan dengan model CIR. Parameter model CIR diduga dengan metode Ordinary Least Square. Model tingkat bunga tersebut digunakan dalam penghitungan premi bersih dan cadangan manfaat asuransi jiwa joint life berdasarkan Tabel Mortalitas Indonesia 2019. Hasil menunjukkan bahwa tingkat bunga BI7DRR dapat dimodelkan dengan baik dengan model CIR. Selain itu, semakin tua usia peserta saat mendaftar asuransi, maka semakin tinggi pembayaran premi bersih, sedangkan cadangan manfaat semakin rendah.

PERAMALAN NILAI TUKAR RUPIAH TERHADAP DOLAR SINGAPURA, BAHT, DAN PESO MENGGUNAKAN METODE GSTAR Retno Budiarti; D. S. Rahmawati; Fendy Septyanto; I Gusti Putu Purnaba
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.20.1.1-13

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 Retno Budiarti; Muhammad Yusuf Sulaiman; I Gusti Putu Purnaba; Windiani Erliana; Berlian Setiawaty; Ruhiyat
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.20.1.15-29

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.

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 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 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 Nabila, Amanda Nahrul Hayati Najib, Mohammad Khoirun 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 Rizki, Kurniadi Ruhiyat Ruhiyat Ruhiyat Ruhiyat Ruhiyat, Ruhiyat S. ARTIKA S. NURDIATI S. UTAMI Sapar . Sapar Sapar Septiany, Rafika Setyawan, Binar Aulia Sri Nurdiati Sugiyanta Sugiyanta Sulaiman, Muhammad Yusuf Syifa Aulia 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 _ Aunuddin

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