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All Journal BIMASTER JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA
Rochmah, Onelia
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Decision Sciences, Operations Research & Management Education Mathematics

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PREDIKSI IMBAL HASIL DAN HARGA SAHAM MENGGUNAKAN GEOMETRIC DAN GEOMETRIC FRACTIONAL BROWNIAN MOTION DENGAN VOLATILITAS Samsir, Rusni; Pratiwi, Yuyun Eka; Rahmawati, Asri; Rochmah, Onelia
BIMASTER : Buletin Ilmiah Matematika, Statistika dan Terapannya Vol 13, No 6 (2024): Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya
Publisher : FMIPA Universitas Tanjungpura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26418/bbimst.v13i6.89745

Abstract

Pemodelan pasar keuangan, khususnya pasar saham, menjadikan model Geometric Brownian Motion (GBM) sebagai elemen penting dalam membangun model statistik. Penelitian ini menawarkan metode untuk meramalkan harga penutupan masa depan perusahaan berukuran kecil dengan menggunakan Geometric Brownian Motion dengan volatilitas stokastik. Model Geometric Fractional Brownian Motion (GFBM) digunakan untuk memodelkan jalur harga aset dengan mengintegrasikan parameter Hurst. Studi ini menganalisis akurasi model GBM dengan volatilitas stokastik dan model GFBM dalam memprediksi harga saham dan imbal hasil berdasarkan simulasi harga saham PGAS. Hasil menunjukkan bahwa model GBM dengan model volatilitas stokastik kanonik (SV-AR(1)) lebih akurat dibandingkan model GFBM untuk mensimulasikan imbal hasil dan jalur harga masa depan pada data yang diberikan.  Kata Kunci : Model Stokastik, Volatilitas, Regresi, Geometric Brownian Motion
Model Matematika Infeksi Hepatitis B dengan Vaksin dan Pengobatan Rochmah, Onelia; Prabasari, Kartika; Rahmawati, Asri
Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika Vol. 12 No. 3 (2025): Jurnal Derivat (Desember 2025)
Publisher : Pendidikan Matematika Universitas PGRI Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31316/j.derivat.v12i3.8256

Abstract

A worldwide public health concern, hepatitis B is brought on by an infection with the Hepatitis B Virus (HBV). HBV can spread when an infected person's blood or bodily fluids come into contact with you. Prevention of HBV infection can be done through two doses of HBV vaccination. Hepatitis B sufferers experience two phases of infection, namely the acute phase and the chronic phase. Hepatitis B sufferers who have entered the chronic phase require treatment to improve recovery. This study aims to model the dynamics of the spread of hepatitis B with the presence of vaccines and treatment. The mathematical model developed consists of seven subpopulations, namely: susceptible (S), first dose vaccine (V1), second dose vaccine (V2), acute (A), chronic (C), treatment (T), and recovered (R). Two equilibrium points are produced by model analysis: the endemic equilibrium point (E1). and the disease-free equilibrium point (E0). The Next Generation Matrix was used to get the Basic Reproduction Number (R0). The analysis's findings suggest that hepatitis B transmission does not spread if R0, as this indicates that the disease-free equilibrium point (E1) is locally asymptotically stable. Conversely, if R0 , then the disease-free equilibrium point (E0) is locally asymptotically unstable, resulting in infection in the susceptible population (S). The dynamics of the mathematical model is demonstrated by numerical simulations. Keywords: Hepatitis B Virus; Mathematical Model; vaccination; treatment.
Co-Authors Asri Rahmawati Prabasari, Kartika Pratiwi, Yuyun Eka Samsir, Rusni