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All Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan
Moch Fandi Ansori
Department Of Mathematics, Faculty Of Science And Mathematics, Universitas Diponegoro
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Model of Deposit and Loan of A Bank Using Spiral Optimization Algorithm Ansori, Moch Fandi; Sidarto, Kuntjoro Adji; Sumarti, Novriana
Journal of the Indonesian Mathematical Society Volume 25 Number 3 (November 2019)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.25.3.826.292-301

Abstract

Nowadays, the study of financial stability of banking is important, which is to observe the behavior of the bank in the future. In this paper, a simple model of deposit and loan of a bank is solved analytically and numerically, and then it is implemented into data of four groups of commercial banks in Indonesia based on their capitals. From the data for each group of banks, the parameters will be estimated using the Spiral Optimization Algorithm. The results show that the algorithm gives satisfactory solutions in terms of closeness between the analytical and numerical solutions. In the long run, the deposit and loan volumes will be stable at their equilibrium points which showing the good condition of the future of the banks based on current state.
ANALYSIS OF BANKING DEPOSIT COST IN THE DYNAMICS OF LOAN: BIFURCATION AND CHAOS PERSPECTIVES Ansori, Moch. Fandi; Hariyanto, Susilo
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 4 (2022): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (452.552 KB) | DOI: 10.30598/barekengvol16iss4pp1283-1292

Abstract

A dynamic model of banking loan based on the gradient adjustment process is presented. The amount of loan that will be channeled in the future depends on the sign of the marginal profit of loan. In this paper, we study the deposit cost in the dynamics of a bank’s loan using bifurcation theory. The analysis shows that the deposit cost can affect the stability of loan equilibrium. If the deposit cost is too high, then the loan equilibrium can lose its stability trough transcritical bifurcation. Meanwhile, if the deposit cost is too low, then the loan equilibrium may lose its stability via flip bifurcation and road to chaos. The loan equilibrium stable if the deposit cost is in between the bifurcation values. These findings are confirmed by the numerical simulations. In addition, we present the graph of Lyapunov exponent to see the existence of chaos and the graph of chaotic loan that is sensitive to the initial condition.
THE ROLE OF COST OF LOAN IN BANKING LOAN DYNAMICS: BIFURCATION AND CHAOS ANALYSIS Ansori, Moch. Fandi; Khabibah, Siti
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 3 (2022): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (723.353 KB) | DOI: 10.30598/barekengvol16iss3pp1031-1038

Abstract

The gradient adjustment process is used to create a dynamic model of banking loan. The sign of the loan’s marginal profit determines how much money will be loaned in the future. In this research, using bifurcation theory, we investigate the cost of loan in the dynamics of a bank’s loan. The results of the analysis indicate that the stability of the loan equilibrium might be impacted by the cost of loan. Loan equilibrium may become unstable through transcritical bifurcation if the cost of the loan is sufficiently high. The loan equilibrium may become unstable through flip bifurcation and path to chaos, however, if the cost of loan is too low. If the cost of loan lies between the bifurcation values, the loan equilibrium is stable. The numerical simulations back up these conclusions. Additionally, we display the Lyapunov exponent graph, which shows the presence of chaos, and the chaotic loan graph, which is sensitive to the initial condition.
LOAN BENCHMARK INTEREST RATE IN BANKING DUOPOLY MODEL WITH HETEROGENEOUS EXPECTATION Ansori, Moch. Fandi
Journal of the Indonesian Mathematical Society Vol. 30 No. 2 (2024): JULY
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.2.1779.205-217

Abstract

A loan benchmark interest rate policy always becomes a challenging problem in the banking industry since it has a role in controlling bank loan expansion, especially when there is competition between two banks. This paper aims to assess the influence of the loan benchmark interest rate on the expansion of loans between two banks. We present a banking duopoly model in the form of two-dimensional difference equations which is constructed from heterogeneous expectation, where one of the banks sets its optimal loan volume based on the other bank’s rational expectation. The model’s equilibrium is investigated, and its stability is analyzed using the Jury stability condition. Investigation indicates that to ensure the stability of the banking loan equilibrium, it is advisable to establish a loan benchmark interest rate that is lower than the flip bifurcation value. Some numerical simulations, such as the bifurcation diagram, Lyapunov exponent, and chaotic attractor, are presented to confirm the analytical findings.
Co-Authors Kuntjoro Adji Sidarto Novriana Sumarti Siti Khabibah susilo hariyanto