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All Journal Jurnal TIMES Zero : Jurnal Sains, Matematika, dan Terapan d'Cartesian: Jurnal Matematika dan Aplikasi Jurnal Informatika dan Rekayasa Perangkat Lunak
Tohap Manurung
Universitas Sam Ratulangi
Agriculture, Biological Sciences & Forestry Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Engineering Mathematics Physics

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Single Index Model in Forming the Optimal Portfolio Before and During the Covid-19 Pandemic on LQ-45 Shares. Vita Indriani Wahyuningsih; Chriestie E.J.C. Montolalu; Tohap Manurung
d\'Cartesian: Jurnal Matematika dan Aplikasi Vol. 10 No. 1 (2021): Maret 2021
Publisher : Sam Ratulangi University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35799/dc.10.1.2021.32979

Abstract

Investment is a commitment to place a number of funds in an asset to gain benefits in the future. but there will be unexpected risks in investment such as the covid-19 pandemic. a strategy to minimize the risk is to form a portfolio. This study aims to form an optimal portfolio before and during the covid-19 pandemic on LQ-45 shares along with the proportion of funds for each share obtained using a single index model. The data used are in the form of daily stock closing prices, JCI price, and risk-free interest rates. The results of this research get a combination of six stocks and the proportion of funds for data before covid-19 are BTPS gets 15.61%, MNCN gets 6.69%, EXCL gets 19.89%, CTRA gets 9.81%, ICBP gets 10.62%, BBCA gets 37.38% and four stocks combination and the proportion of funds for data during covid-19 are INCO gets 30.09%, ANTM gets 27.54%, INKP gets 22.81%, KLBF gets 19.56%. INCO, ANTM, INKP, KLBF shares can be considered by investors in making investment decisions during the covid-19 pandemic.
Distribution Models of Claim Frequency and Claim Severity in Determining the Pure Premium of Car Insurance with the Application of a Deductible Tohap Manurung
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 2 (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.v9i2.26257

Abstract

The objective of this study is to determine the pure premium value based on a car damage claim data model from car insurance company X, using data that applies a deductible value. The data used comprises car damage claims with deductibles applied during a year period. Determining the distribution model for insurance claims is one of the relevant techniques for measuring operational risk in insurance companies. In this context, historical claim data is tested against existing distribution models, enabling the calculation of pure premium values for the insurance company. The results show that the claim frequency data follows a Negative Binomial distribution with an expected value of E(N) = 0.0107, and the claim severity data follows a Log-logistic distribution with E(X) = 12,037,950. Therefore, the calculated pure premium value is E(S) = Rp129,205.19. The pure premium obtained serves as the basis for determining the actual premium charged to policyholders, with the addition of loadings.
Website-Based Running Sports Information System For Communities In North Sulawesi Using Extreme Programming Method Inayah Syaban; Tohap Manurung; Aditya Kalua; Eric Alfonsius
Jurnal Informatika dan Rekayasa Perangkat Lunak Vol. 6 No. 4 (2025): Volume 6 Number 4 Desember 2025
Publisher : Universitas Teknokrat Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33365/jatika.v6i4.692

Abstract

The community in North Sulawesi has shown a strong interest in running, as evidenced by the increasing number of running communities and events. However, the absence of an integrated platform that provides information about running routes, communities, and events has become a challenge for runners in accessing information efficiently. This study employs the Extreme Programming method and aims to develop a web-based information system that delivers comprehensive information related to running sports. The website features key components such as community profile pages, a running event calendar, and running route locations, complete with maps, route descriptions, track lengths, difficulty categories, photo galleries, and supporting facilities like toilets and resting spots. The displayed information is sourced from various local communities and is systematically organized to ensure easy access for the public. Additionally, the website includes a contact page that allows users to provide suggestions or feedback to the admin. It also features a function that enables event organizers to directly submit event data and running route locations into the system through the contact page. This system is expected to help the community access information more easily and increase participation in running activities throughout North Sulawesi
ANALISIS SURVIVAL DENGAN METODE NELSON–AALEN UNTUK PENENTUAN PREMI BERSIH ASURANSI JIWA SEUMUR HIDUP PADA PENDERITA GAGAL GINJAL Lidya Priska Dupa; Tohap Manurung; John Socrates Kekenusa; Eliasta Ketaren
Jurnal TIMES Vol 15 No 1 (2026): Jurnal TIMES
Publisher : STMIK TIME

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.51351/jtm.15.1.2026951

Abstract

Kementerian Kesehatan dan Indonesian Renal Registry mencatat bahwa lebih dari 134.000 pasien menjalani hemodialisis akibat gagal ginjal pada tahun 2024, yang menunjukkan tingginya prevalensi penyakit ini serta implikasinya terhadap aspek kesehatan dan keuangan. Penelitian ini bertujuan untuk menentukan peluang ketahanan hidup menggunakan metode Nelson–Aalen dan menghitung premi bersih asuransi jiwa seumur hidup bagi penderita gagal ginjal usia 35 hingga 75 tahun. Data diperoleh dari data akumulasi pasien penderita gagal ginjal yang dipublikasikan pada jurnal Indonesian Council of Premier Statistical Science. Estimasi fungsi hazard kumulatif dilakukan dengan pendekatan Nelson–Aalen, lalu digunakan untuk memperoleh fungsi survival sebagai dasar analisis ketahanan hidup. Hasil menunjukkan bahwa estimasi peluang ketahanan hidup pasien penderita gagal ginjal sebesar 55,438%. Berdasarkan estimasi survival, tingkat suku bunga 5%, dan santunan sebesar Rp150.000.000,00, didapatkan premi bersih asuransi jiwa seumur hidup untuk usia 35 tahun, sebesar Rp 63.755.240,18 bagi laki‑laki dan Rp 63.730.011,13 bagi perempuan, sedangkan pada usia 75 tahun masing‑masing sebesar Rp 65.601.981,23 dan Rp 65.227.734,90. Hasil ini menunjukkan bahwa premi meningkat seiring pertambahan usia, yang selaras dengan menurunnya peluang ketahanan hidup dan meningkatnya risiko kematian pada usia yang lebih tinggi.
PENENTUAN DAN ANALISIS HARGA OPSI TIPE EROPA MENGGUNAKAN MODEL BLACK-SCHOLES: STUDI KASUS PADA SAHAM AMAZON.COM INC. Geraldy Franklin Pesak; Tohap Manurung; Jullia Titaley; Eliasta Ketaren
Jurnal TIMES Vol 15 No 1 (2026): Jurnal TIMES
Publisher : STMIK TIME

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.51351/jtm.15.1.2026952

Abstract

Opsi saham merupakan kontrak derivatif yang memberikan hak (bukan kewajiban) untuk membeli atau menjual saham underlying pada harga dan waktu tertentu, sehingga memerlukan metode valuasi yang andal. Penelitian ini bertujuan menentukan harga teoretis opsi call dan put menggunakan model Black-Scholes, menguji akurasi model melalui perbandingan dengan harga pasar aktual, serta menganalisis sensitivitas harga opsi menggunakan parameter The Greeks. Penelitian ini menggunakan data sekunder berupa harga saham AMZN (S=$210,11), variasi strike price (K =$85 sampai $370), tingkat suku bunga bebas risiko, volatilitas historis, dan waktu jatuh tempo. Berdasarkan hasil perhitungan, diperoleh harga teoretis opsi call yang menurun secara monoton dari $127,56 pada K = 85 menjadi $1,68 pada K = 370, sedangkan opsi put menunjukkan tren sebaliknya dari $0,02 menjadi $151,02, konsisten dengan prinsip ekonomi moneyness. Validasi model untuk opsi call menghasilkan MAE sebesar 2,18, MAPE 5,32%, dan RMSE 5,20. sementara itu, pada opsi put diperoleh nilai MAE sebesar 4,78, MAPE 25,63%, dan RMSE 7,44. Nilai tersebut menunjukkan bahwa model memberikan tingkat akurasi yang lebih tinggi pada penentuan harga opsi call dibandingkan pada opsi put. Analisis The Greeks menunjukkan bahwa Delta merupakan parameter yang paling berpengaruh terhadap harga opsi. Nilai Delta yang mendekati 1 menunjukkan bahwa perubahan harga saham memberi dampak paling besar terhadap perubahan harga opsi.
Co-Authors Aditya Kalua Alfonsius, Eric Chriestie E.J.C. Montolalu Eliasta Ketaren Geraldy Franklin Pesak Inayah Syaban John Socrates Kekenusa Jullia Titaley Lidya Priska Dupa Vita Indriani Wahyuningsih