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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) Limits: Journal of Mathematics and Its Applications Jambura Journal of Mathematics 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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Penghitungan Premi Asuransi Kendaraan Bermotor Menggunakan Generalized Linear Models dengan Distribusi Tweedie Tri Andika Julia Putra; Donny Citra Lesmana; I Gusti Putu Purnaba
Jambura Journal of Mathematics Vol 3, No 2: July 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

ABSTRAKSeorang aktuaris mempunyai tugas penting dalam menentukan harga premi yang sesuai untuk setiap nasabah dengan risiko dan karakteristik yang berbeda. Banyak variabel yang dapat mempengaruhi harga premi. Oleh karena itu, aktuaris harus mengetahui variabel-variabel yang berpengaruh signifikan terhadap premi. Tujuan dari penelitian ini adalah untuk menentukan variabel yang dapat mempengaruhi besaran premi murni menggunakan distribusi campuran dalam menentukan besarnya premi melalui Generalized Linear Models (GLM) serta menentukan model harga premi yang sesuai berdasarkan variabel-variabel yang mempengaruhinya. Salah satu analisis statistik yang dapat digunakan untuk memodelkan premi asuransi adalah Generalized Linear Models. GLM merupakan perluasan dari model regresi klasik yang dapat mengakomodasi fleksibilitas untuk menggunakan beberapa distribusi data tetapi terbatas pada distribusi keluarga eksponensial. Dalam model GLM, premi diperoleh dengan mengalikan nilai ekspektasi bersyarat dari frekuensi klaim dan biaya klaim. Berdasarkan penelitian yang telah dilakukan diketahui bahwa frekuensi klaim dan besarnya klaim mengikuti distribusi Tweedie. Dari kedua model tersebut diketahui bahwa variabel yang mempengaruhi premi murni adalah jumlah anak, pendapatan per bulan, status pernikahan, pendidikan, pekerjaan, penggunaan kendaraan, besarnya bluebook yang dibayarkan, dan jenis kendaraan nasabah. Hal ini menunjukkan bahwa model GLM merupakan model yang representatif dan berguna bagi perusahaan asuransi. ABSTRACTIt is an important task for an actuary in determining the appropriate premium price for each customer with different risks and characteristics. Many variables can affect the premium price. Therefore, actuaries must determine the variables that significantly affect the premium. The purpose of this study is to determine the variables that can affect the amount of pure premium using a mixed distribution in determining the amount of premium through Generalized Linear Models (GLM) and determine the appropriate premium price model based on the variables that influence it. One of the statistical analyzes that can be used to model insurance premiums is the Generalized Linear Models. GLM is an extension of the classic regression model that can accommodate the flexibility of its users to use multiple data distributions but is limited to the exponential family distribution. In the GLM model, the premium is obtained by multiplying the conditional expected value of the frequency of claims and the cost of claims. Based on the research that has been done, it is known that the frequency of claims and the size of claims follow the Tweedie distribution. From the two models, it is known that the variables affecting the pure premium are the number of children, monthly income, marital status, education, occupation, vehicle use, the number of bluebooks paid, and the type of vehicle from the customer. This shows that the GLM model is a representative and useful model for the insurance company business.

Sifat Kemonotonan Barisan Trapezoid Sum dari Kelas Fungsi Nonkonveks dan Nonkonkaf Yudasril Yudasril; Berlian Setiawaty; I Gusti Putu Purnaba
Limits: Journal of Mathematics and Its Applications Vol 19, No 1 (2022)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v19i1.9218

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.

MENENTUKAN PREMI ASURANSI JIWA JOINT LIFE UNTUK TIGA ORANG TERTANGGUNG Vivin Manjaruni; I Gusti Putu Purnaba
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.v3i1.8331

Dampak Covid-19 di tahun 2020 mengakibatkan masyarakat rentan untuk terserang penyakit bahkan bisa sampai meninggal dunia. Hal ini berdampak pada kerugian finansial akibat biaya perawatan di rumah sakit yang tidak sedikit. Oleh sebab itu, dengan penggunaan asuransi jiwa akan melindungi keluarga dari kerugian finansial dengan adanya santunan atau uang pertanggungan yang akan diberikan oleh perusahaan asuransi. Asuransi jiwa joint life adalah jenis asuransi yang dapat membayar premi saat kematian pertama salah satu pihak yang dipertanggungkan. Berdasarkan kebutuhan masyarakat Indonesia di tengah pandemi sekarang, maka asuransi jiwa yang sesuai adalah jenis asuransi jiwa joint life. Penelitian ini bertujuan untuk mengetahui jumlah premi tahunan asuransi jiwa joint life untuk satu rumah tangga beranggotakan tiga orang yang terdiri dari sepasang suami istri dan satu putra mereka, dengan menggunakan formula premi tahunan. Selain itu, penelitian ini juga bertujuan untuk membandingkan apakah tua mudanya usia seorang suami mempengaruhi besar kecilnya biaya premi yang harus dibayarkan. Berdasarkan hasil perhitungan dan perbandingan yang diteliti maka suami 30 tahun, istri 30 tahun dan putra 10 tahun dengan masa asuransi 5 tahun dan besar santunan 1 rupiah serta tingkat bunga 6% akan membayar premi 0,1893 rupiah yang lebih kecil dibandingkan dengan usia suami di atas 30 tahun menggunakan Tabel Mortalita Indonesia Tahun 2019.

Pengaruh Inflasi terhadap Strategi Optimal Investasi dan Konsumsi dengan Model Stokastik Dara Irsalina; Retno Budiarti; I Gusti Putu Purnaba
Limits: Journal of Mathematics and Its Applications Vol 19, No 1 (2022)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v19i1.9987

The aim of this study is to investigate an optimal investment-consumption strategy under inflation rate with interest rate is described by Cox-Ingersol-Ross (CIR) model and volatility of the stock price is defined by Heston’s volatility model. A dynamic programming principle is used to obtain a Hamilton Jacobi Bellman (HJB) equation for the value function and choose a power utility function as utility function. The explicit solution of optimal investment and consumption are acquired with using separate variable and approach variable technique. The parameter’s values are approached by Euler-Maruyama method and Ordinary Least Square (OLS) method. Assumed that the portfolio of the investor contains a risk-free asset and a risk asset. Monthly historical data of TLK stock is used as risk asset and monthly historical data of BI 7-Day (Reverse) Repo Rate (BI7DRR) is used as risk-free asset, we obtain that the proportion of investment in stock is directly proportional to return of stock and the inflation rate does not have an impact on proportion investment in the stock. Meanwhile the optimal consumption of wealth is directly proportional to investor’s wealth and inversely proportional with inflation rate, which is the investor should consume less money of his wealth when the inflation rate increases.

Penentuan Premi Tunggal Bersih pada Reversionary Annuity untuk Pasangan Suami Istri dengan Model Frank’s Copula Furlo Gilbert Godfrey; I Gusti Putu Purnaba; Ruhiyat Ruhiyat
Jambura Journal of Mathematics Vol 4, No 2: July 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

One of the multi-life annuity products is a reversionary annuity, a life annuity product for two insured people. The annuity payment for this product will begin after one of the insured specified in the contract dies first until the other insured dies as well. The calculation of the annuity premium is usually done by assuming independence between the random variable of remaining life-times of the insured parties. However, this is not relevant to the actual situation because the husband and wife are interrelated with their lives. This study considered this relationship when modelling the joint distribution of the remaining life-times between husband and wife. Frank’s copula was used to model the joint distribution of the remaining life-times of husband and wife. It was built from marginal distribution, which was assumed to follow the mortality value in the 2019 Indonesian Mortality Table IV. The mortality value at non-integer ages was assumed to follow a uniform distribution (uniform distribution of death). Furthermore, the joint survival distribution modelled by copula was constructed exactly when husband and wife are married. This study also considered the net single premium of reversionary annuity for several beneficiary cases. In general, the results of the calculation of the net single premium with Frank’s copula produced a lower value than the calculation of the assumption of independence for all beneficiary cases. In addition, the purchase time of an annuity also affects the net single premium, which increases up to a certain point of marriage age and then decreases thereafter.

Faktor-Faktor yang Mempengaruhi Perilaku Nelayan Artisanal Dalam Pemanfaatan Sumberdaya Perikanan di Pantai Utara Provinsi Jawa Barat Prihandoko, Prihandoko; Jahi, Amri; Gani, Darwis S.; Purnaba, I Gusti Putu; Adrianto, Luky; Tjitradjaja, Iwan
Makara Human Behavior Studies in Asia Vol. 15, No. 2
Publisher : UI Scholars Hub

Show Abstract | Download Original | Original Source | Check in Google Scholar

This study aims to estimate accurately the behavior using the Theory of Planned Behavior perspective of artisanal fishermen in Indonesia, in the midst of life with the condition of degradation of marine resources are declining, absolute poverty faced by artisanal fishermen and the more complex issues of coastal resource use in Indonesia with a more diversity of stakeholders utilizing these resources. The population of artisanal fishermen in the northern coast of West Java Province 10,404. Techniques for sampling by cluster random sampling clusters with the number of household sample of 400 artisanal fishermen. Data was collected using a questionnaire interview further processed using the program structural equation model (SEM) and LISREL 8:54. The conclusion of this study were (1) Theory of planned behavior perspective can be used to view the intention to behave and conduct artisanal fishermen in the northern coast of West Java province, despite the possible existence of behavior that is done without the intention to behave (2) the coefficient of determination between the attitude variables, subjective norm, perceived behavior control to variable behavior intention at 0.40. These conditions indicate the existence of other variable factors of 60% outside variables that affect the intention of this study to behave. Meanwhile the influence of variables on behavior intention to behave by 0.51 indicates that it is not fully manifested the intention to behave in accordance with the behavior of fishermen in their fishing activities, (3) that explains the study's findings about the factors that influence the behavior of artisanal fishermen in the utilization fishery resources, can contribute to the activities of co-management of fisheries in Indonesia, especially in communities in the study area on the northern coast of West Java Province

PENGHITUNGAN KREDIBILITAS DENGAN PUSTAKA ACTUAR DALAM R I. MAULIDI; W. ERLIANA; A. D. GARNADI; S. NURDIATI; I G. P. PURNABA
MILANG Journal of Mathematics and Its Applications Vol. 16 No. 2 (2017): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Teori Kredibilitas (Credibility Theory) merupakan perangkat penting dalam pekerjaan aktuaria. Dengan menggunakan Kredibilitas dapat diduga besarnya pembayaran premi atau banyaknya klaim yang akan terjadi di masa mendatang secara kredibel. Dalam tulisan ini akan diperkenalkan konsep dalam teori kredibilitas dan aplikasinya dengan menggunakan paket Actuar yang ditulis menggunakan software R.

PENDUGAAN PARAMETER DAN KEKONVERGENAN PENDUGA PARAMETER MODEL POISSON HIDDEN MARKOV M. FIKRI; B. SETIAWATY; I G. P. PURNABA
MILANG Journal of Mathematics and Its Applications Vol. 15 No. 1 (2016): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Model hidden Markov terdiri dari sepasang proses stokastik yaitu proses observasi dan proses yang memengaruhi observasi. Proses stokastik yang memengaruhi observasi ini diasumsikan membentuk rantai Markov dan tidak diamati. Model Poisson hidden Markov (MPHM) adalah salah satu model hidden Markov diskret dan proses observasinya jika diketahui proses yang memengaruhinya diasumsikan menyebar Poisson. Salah satu ciri MPHM adalah bersifat overdispersi, yaitu ragam data lebih besar dari rataannya. Permasalahan utama MPHM ialah menduga parameter yang memaksimumkan fungsi likelihood. Fungsi likelihood dihitung menggunakan algoritme Forward-Backward. Algoritme Expectation Maximization (algoritme EM) digunakan untuk memaksimumkan fungsi likelihood. Penduga parameter MPHM yang diperoleh menggunakan algoritme EM konvergen ke titik stasioner dari fungsi likelihood.

ESTIMATING THE INTENSITY IN THE FORM OF A POWER FUNCTION OF AN INHOMOGENEOUS POISSON PROCESS I W. MANGKU; I. WIDIYASTUTI; I G. P. PURNABA
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 1 (2005): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

An estimator of the intensity in the form of a power function of an inhomogeneous Poisson process is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indeﬁnitely expands. The asymptotic bias, variance and the mean- squared error of the proposed estimator are computed. Asymptotic normality of the estimator is also established.

ANALISIS RISIKO OPERASIONAL MENGGUNAKAN PENDEKATAN DISTRIBUSI KERUGIAN DENGAN METODE AGREGAT Y. ARBI; R. BUDIARTI; I G. P. PURNABA
MILANG Journal of Mathematics and Its Applications Vol. 10 No. 2 (2011): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes or external problems. Insurance companies as financial institution that also faced at risk. Recording of operating losses in insurance companies, were not properly conducted so that the impact on the limited data for operational losses. In this work, the data of operational loss observed from the payment of the claim. In general, the number of insurance claims can be modelled using the Poisson distribution, where the expected value of the claims is similar with variance, while the negative binomial distribution, the expected value was bound to be less than the variance.Analysis tools are used in the measurement of the potential loss is the loss distribution approach with the aggregate method. In the aggregate method, loss data grouped in a frequency distribution and severity distribution. After doing 10.000 times simulation are resulted total loss of claim value, which is total from individual claim every simulation. Then from the result was set the value of potential loss (OpVar) at a certain level confidence.

Co-Authors A. D. GARNADI Adilla, Indrya Amiruddin Saleh Amri Jahi Amri Jahi Amri Jahi Auliya Fithry Aunuddin . Awatif Berlian Setiawaty Binar Aulia Setyawan D. C. LESMANA D. S. Rahmawati Dara Irsalina 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 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 Iwan Tjitradjaja Iwan Tjitradjaja Iwan Tjitradjaja J. S. SELEKY Kelvin Gunawan Khairiati, Alfi Kumala Intansari Laila Qudrah Fikriyah Luky Adrianto M. FIKRI Ma'mun Sarma Maharani, Ardella Manjaruni, Vivin Aprilia Mokhamad O Royani Muh Hatta Jamil Muhammad Yusuf Sulaiman Nahrul Hayati 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 Retno Budiarti Rizki, Kurniadi Ruhiyat Ruhiyat Ruhiyat Ruhiyat Ruhiyat, Ruhiyat S. ARTIKA S. NURDIATI S. UTAMI Sapar . Sapar Sapar Septiany, Rafika Sugiyanta Sugiyanta Sulaiman, Muhammad Yusuf 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 Yudasril _ Aunuddin

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