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All Journal Journal of the Indonesian Mathematical Society JURNAL ILMIAH MATEMATIKA DAN TERAPAN
Eka, M
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Mathematics

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Analisis Kontrol Optimal Pada Model Matematika Penyebaran Pengguna Narkoba Dengan Faktor Edukasi Resmawan; Eka, M; Nurwan; Achmad, N
JURNAL ILMIAH MATEMATIKA DAN TERAPAN Vol. 17 No. 2 (2020)
Publisher : Program Studi Matematika, Universitas Tadulako

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22487/2540766X.2020.v17.i2.15201

Abstract

ABSTRACT This paper discusses the mathematical model of drug users with education. Optimal control theory was used on this model with education as a control to achieve the goal of minimizing the number of drug users. The optimal control problem was analyzed using Pontryagin’s minimum principle and performed numerical simulation by using a 4th-order Runge-Kutta method. Based on the numerical simulation, there was a change in the number in each population which caused the population with education to increase, and control with education resulted in the reduced number of drug users. Keywords: Optimal control; mathematical model; drug users; education ABSTRAK Artikel ini membahas tentang model matematika penyebaran pengguna narkoba dengan faktor edukasi. Teori kontrol optimal diterapkan pada model ini dengan pemberian kontrol berupa edukasi dengan tujuan untuk meminimumkan jumlah pengguna narkoba. Kontrol optimal dianalisis menggunakan Prinsip Minimum Pontryagin dan dilakukan simulasi numerik dengan menggunakan metode Runge-Kutta orde 4. Berdasarkan simulasi diperoleh bahwa terjadi perubahan jumlah di tiap populasi dan mengakibatkan jumlah populasi dengan edukasi bertambah, serta pemberian kontrol dengan edukasi mengakibatkan jumlah pengguna narkoba berkurang. Kata kunci : Kontrol optimal; model matematika; pengguna narkoba; edukasi
Premiums of Deposit Insurance with Maximum Limit Under the Black-Scholes Model Puspita, Dila; Delima, Anggun Citra; Mukhaiyar, Utriweni; Eka, Maharani; Azis, Rheznandya Arkaputra
Journal of the Indonesian Mathematical Society Vol. 31 No. 2 (2025): JUNE
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i2.1792

Abstract

Deposit insurance is an important mechanism in protecting bank customers from the risk of bankruptcy and providing a sense of security for their savings. Under deposit insurance, customers will still receive a refund of their funds up to a certain limit determined by the deposit insurance agency. This research aims to construct a formula to calculate the premium of deposit insurance with a given upper claim limit. To the best of the authors' knowledge, this article is the first study that gives a formula for deposit insurance premiums with a coverage limit. First, we present a theorem that shows the equivalence between the claim of deposit insurance with coverage limit with the payoff of two put options. Secondly, under the assumption that the asset follows Geometric Brownian Motion, we determine the fair price of the premium of deposit insurance. The main research findings indicate that the sum of two Black-Scholes options with different strike prices can be used to determine the premium value of deposit insurance while considering the applied coverage limits. Finally, we simulate some sensitivity analysis to gain a deeper understanding on the impact of several important variables on the magnitude of premium. Based on sensitivity analysis, it is found that the premium value is inversely proportional to interest rates and directly proportional to asset price volatility.
Co-Authors Achmad, N Azis, Rheznandya Arkaputra DELIMA, ANGGUN CITRA Nurwan Puspita, Dila Resmawan Resmawan Utriweni Mukhaiyar