OPTIMAL CONTROL IN BANKING MATHEMATICAL MODELS TO MAXIMIZE PROFIT.

• Main Author: Nathanael Christidyawan, Hubert
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/84122
• Institution: Institut Teknologi Bandung

In the banking sector, fund management and lending are two primary activities that significantly impact profitability. Banks must balance risk and profitability, often involving strategic decisions in resource allocation. This thesis explores the application of optimal control in a mathematical banking model to maximize profit. The model is based on a system of differential equations that describe the dynamics of deposits, loans, and bank equity. The methodology employed includes the application of Pontryagin’s Maximum Principle (PMP) and the Forward-Backward Sweep method to determine the optimal strategy for setting deposit and loan interest rates. PMP is applied to obtain optimal conditions and to define the control policies that the bank should implement, with the controls being the deposit interest rate and loan interest rate. Numerical simulations are conducted to test the effectiveness of this approach in practical scenarios. There are control value constraints that must be adhered to in order to maintain the stability of deposit rates, loans, and equity. Additionally, constraints arise from Bank Indonesia regulations, requiring adjustments to the control value limits. Numerically, the profit rate shows an increase ranging from 11.88% to 16.67% over time compared to before control was implemented. Additionally, sensitivity analysis identifies key parameters that influence the model’s performance, with important implications for strategic banking decision-making.