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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) JTAM (Jurnal Teori dan Aplikasi Matematika) Milang Journal of Mathematics and Its Applications
Fendy Septyanto
IPB University
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Electrical & Electronics Engineering Mathematics

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Color code techniques in rainbow connection Fendy Septyanto; Kiki A. Sugeng
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 6, No 2 (2018): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2018.6.2.14

Abstract

Let G be a graph with an edge k-coloring γ : E(G) → {1, …, k} (not necessarily proper). A path is called a rainbow path if all of its edges have different colors. The map γ is called a rainbow coloring if any two vertices can be connected by a rainbow path. The map γ is called a strong rainbow coloring if any two vertices can be connected by a rainbow geodesic. The smallest k for which there is a rainbow k-coloring (resp. strong rainbow k-coloring) on G is called the rainbow connection number (resp. strong rainbow connection number) of G, denoted rc(G) (resp. src(G)). In this paper we generalize the notion of “color codes” that was originally used by Chartrand et al. in their study of the rc and src of complete bipartite graphs, so that it now applies to any connected graph. Using color codes, we prove a new class of lower bounds depending on the existence of sets with common neighbours. Tight examples are discussed, involving the amalgamation of complete graphs, generalized wheel graphs, and a special class of sequential join of graphs.
BILANGAN KETERHUBUNGAN PELANGI PADA SEQUENTIAL JOIN DARI EMPAT DAN LIMA GRAF Fendy Septyanto
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (344.014 KB) | DOI: 10.29244/milang.18.1.77-85

Abstract

Pewarnaan pelangi pada suatu graf adalah pelabelan busur sehingga setiap pasang simpul dapat dihubungkan oleh lintasan pelangi (lintasan yang warna busurnya berbeda semua). Bilangan keterhubungan pelangi dari suatu graf adalah banyaknya warna minimal pada pewarnaan pelangi pada graf tersebut. Sequential join dari beberapa graf saling lepas diperoleh dengan menghubungkan setiap simpul pada graf pertama ke setiap simpul pada graf kedua, lalu setiap simpul pada graf kedua ke setiap simpul pada graf ketiga, dan seterusnya. Penelitian ini menyelidiki bilangan keterhubungan pelangi pada sequential join dari empat atau lima graf.
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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (387.725 KB) | 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.
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

Abstract

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.
Modelling Dependencies of Stock Indices During Covid-19 Pandemic by Extreme-Value Copula Retno Budiarti; Kumala Intansari; I Gusti Putu Purnaba; Fendy Septyanto
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. 
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

Abstract

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.
Co-Authors Berlian Setiawaty D. S. Rahmawati I Gusti Putu Purnaba I Gusti Putu Purnaba I Gusti Putu Purnaba Indrya Adilla Kiki A. Sugeng Kumala Intansari Retno Budiarti Retno Budiarti Ruhiyat Ruhiyat Windiani Erliana Windiani Erliana Yuda Ardiansyah