Individual microcredit loyalty contract: Markov modeling and stationary viability[Contrat de microcrédit individuel à fidélisation : Modélisation markovienne et viabilité stationnaire]

Starting from the generalized model of Osman Khodr and Francine Diener [3], we present a model that meets the expectations of the microfinance institution (MFI) and that of borrowers and that incorporates all the characteristics of poor populations, know the tolerance in case of partial default and the possibility of having a progressive loan automatically. It is a learning model that will offer microfinance institutions a decision support tool more suited to their reality. It is based on a Markov chain which includes several states associated with the economic situation of the borrower including three types of beneficiaries: B_1 is the state of being beneficiary at initial time t = 1, B_2 is the state of being beneficiary at time t = 2, and I is the state of financial inclusion which means permanent beneficiary, A^1 the state of applicant and A^T … A^2 represent (T - 1) states of exclusion. We have modeled the behavior of a borrower by a parameter λ which depends on the probability α of success of the borrower. At the initial moment, λ= (1+α)/(1-α), this quantity changes as soon as the borrower passes from one state to another with a probability of success different from α. The agency's decision to grant credit depends entirely on the parameter λ which is compared to the set subjective threshold values. The chance γ of having a loan (γ: probability of requesting credit granted) for a borrower depends on the parameter γ, with γ=1-1/λ, λ≠0. keywords: Microfinance, Credit Grant Decision, Markov Chain, Individual Loan, Dynamic Incentive, Updated Expected Profit