Markov chain representation of individual and group lending in microcredit

PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations Pub Date : 2019-12-19 DOI:10.1063/1.5139150

Trisha Therese R. Bernardino, Jasmin-Mae B. Santos

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Abstract

Microcredit is a financial tool that provides small amounts of loan to low-income or poor people. An individual or a group can enter microlending and is expected to pay after an agreed period. In this research, a probabilistic approach through Markov chain representations of repayment processes for individual and group lending of two borrowers is revisited; and conditions for absence of strategic default are identified. Results are then extended to the case of three borrowers, as a Markov chain model is presented and a formula for the expected total discounted return of a borrower is obtained.Microcredit is a financial tool that provides small amounts of loan to low-income or poor people. An individual or a group can enter microlending and is expected to pay after an agreed period. In this research, a probabilistic approach through Markov chain representations of repayment processes for individual and group lending of two borrowers is revisited; and conditions for absence of strategic default are identified. Results are then extended to the case of three borrowers, as a Markov chain model is presented and a formula for the expected total discounted return of a borrower is obtained.

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小额信贷中个人和团体贷款的马尔可夫链表示

小额信贷是一种向低收入者或穷人提供小额贷款的金融工具。个人或团体可以进入小额贷款，并在约定的期限后付款。在本研究中，通过马尔可夫链表示的概率方法对两个借款人的个人和团体贷款的还款过程进行了重新审视;并确定了不存在战略违约的条件。然后将结果推广到三个借款人的情况，给出了马尔可夫链模型，并得到了借款人期望总贴现收益的公式。小额信贷是一种向低收入者或穷人提供小额贷款的金融工具。个人或团体可以进入小额贷款，并在约定的期限后付款。在本研究中，通过马尔可夫链表示的概率方法对两个借款人的个人和团体贷款的还款过程进行了重新审视;并确定了不存在战略违约的条件。然后将结果推广到三个借款人的情况，给出了马尔可夫链模型，并得到了借款人期望总贴现收益的公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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PROCEEDINGS OF THE 8TH SEAMS-UGM INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATIONS 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations

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