MATHEMATICAL MODELING AND ANALYSIS OF BANK CAPITAL ADEQUACY DYNAMICS

Abstract

Maintaining adequate capitalization is paramount for banks to ensure financial stability and regulatory compliance. This paper employs the Differential Transform Method (DTM) to solve a proposed dynamic model of bank capital adequacy, focusing on the relationship between a bank’s capital and its risk-weighted assets (RWAs). Three settings of RWAs growth, namely constant, linearly increasing, and exponentially increasing, are explored, with their respective parameter setups embedded. The effectiveness of the DTM is validated through comparisons of the obtained solutions with their corresponding exact solutions, demonstrating its ability to accurately simulate capital adequacy dynamics under varying RWAs growth patterns. The equilibrium analysis reveals that the steady-state level of capital adequacy is directly proportional to the bank’s assets, emphasizing the importance of asset growth for financial stability. Stability analysis indicates that a positive decay rate is crucial for resilience against perturbations. These findings underscore the application of mathematical modeling using DTM in aiding banks’ capital management strategies amidst evolving financial landscapes, ensuring they maintain adequate capital levels and respond effectively to economic shocks.