Mathematical Modeling of Bank Loan Allocation Using Dynamic Programming: The Case of Bank Al-Maghrib in 2023

ABSTRACT: This applied study aims to implement a precise mathematical model that enhances the efficiency of financial resource allocation within banking institutions. The model is based on dynamic programming, which is considered one of the most important quantitative methods for making optimal decisions over successive time periods. The core idea revolves around distributing the available financial balance progressively, taking into account present-time preference and the time value of money. The study relies on actual quarterly data of bank loans during the third quarter of 2023, where the total allocated balance amounted to 549,920 million dirhams, distributed among three main types of loans: investment loans, real estate loans, and consumer loans. The applied model includes a logarithmic utility function that reflects the diminishing marginal utility with the increase in used resources. The model also integrates both the discount factor (β = 0.95) and the interest rate (r = 0.05) to estimate the optimal allocations for the next three future periods. This model serves as a reference tool that enables comparison between the actual allocations adopted by the bank and those derived from the theoretical model, opening the door for better strategic decisions and more rational budget management.