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Abstract
Microcredit is a method of lending small amounts of money to low-income individuals who have no access to traditional financial institutions. Upon applying for a loan, an individual may either be able to repay it and be granted a loan again, otherwise s/he demands for a new loan. These events influence certain factors, which can be illustrated through a hidden Markov model (HMM). This study provides a hidden Markov representation of microcredit taking into consideration the borrower's acquisition of small businesses. Model algorithms used in addressing the problems in HMM, such as the Viterbi algorithm, are discussed and implemented via numerical examples.
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References
- Awad, M. and Khanna, R., “Efficient learning machines: theories, concepts, and applications for engineers and system designers”, Springer nature, (2015).
- Bernardino, T. T. and Santos, J.M., “Markov chain representation of individual and group lending in microcredit”, AIP Conference Proceedings 2192(1) (2019), 060004-1 - 060004-13. https://doi.org/10.1063/1.5139150.
- Diener, F., Diener, M., Khodr, O., and Protter, P., “Mathematical models for microlending”, Proceedings of the 16th Mathematical Conference of the Bangladesh Mathematical Society Volume 1 (2009).
- Diener, F. and Khodr, O., “Mathematical models for individual and group lending in microfinance”, Universit´e de Nice, Laboratoire de Math´ematiques (2008), https://math.univ-cotedazur.fr/ diener/Mifi/papierKodrDiener.pdf.
- Dulay, S., “Markov chain models of microcredit and the application of the perron-frobenius theorem”, BS Thesis, Institute of Mathematics, University of the Philippines Diliman (2018).
- Giampieri, G., Davis, M., and Crowder, M. “Analysis of default data using hidden Markov models”, Quantitative Finance, 5(1) (2005), 27–34. https://doi.org/10.1080/14697680500039951
- Frazzoli, E., “Principles of Autonomy and Decision Making”, University Lecture, Massachusetts Institute of Technology (2010).
- Giva, M.A., “Hidden markov representation of microcredit”, BS Thesis, Institute of Mathematics, University of the Philippines, Diliman (2023).
- Hassan, R., and Nath, B., “Stock market forecasting using hidden Markov model: A new approach”, Proceedings of the 2005 5th International Conference on Intelligent Systems Design and Applications (2003).
- Jurafsky, D. and Martin, J., “Speech and language processing”, https://web.stanford.edu/ jurafsky/slp3/A.pdf, Accessed: 03-05-2023.
- Kamath, H. and Jahan, N. F., “Using hidden markov model to monitor possible loan defaults in banks”, International Journal of Economics & Business Administration Vol. 0(4) (2020), 1097-1107.
- Li, N., “Hidden markov model and financial application” Master’s thesis, The University of Texas at Austin (2016).
- Ntwiga, D.B., Ogutu, C., and Kirumbu, M.K., “Inclusion of peer group and individual low-income earners in m-shwari micro-credit lending: a hidden markov model approach”, International Journal of Electronic Finance 9(2) (2018), 121-133.
- Ntwiga, D.B., Ogutu, C., Kirumbu, M.K., and Weke, P., “A Hidden Markov Model of Risk Classification among the Low Income Earners”, Journal of Finance and Economics, 6(6) (2018), 242-249. https://doi.org/10.12691/jfe-6-6-6
- Ntwiga, D.B. and Weke, P., “Credit Scoring for M-Shwari using Hidden Markov Model”, European Scientific Journal, ESJ, 12(15) (2016), 176. https://doi.org/10.19044/esj.2016.v12n15p176
- Rabiner, L., “A tutorial on hidden markov models and selected applications in speech recognition” Proceedings of the IEEE 77(2) (1989), 257–286.
- Ramage, D., “Hidden markov models fundamentals”, CS229 Section Notes (2007), https://cs229.stanford.edu/section/cs229-hmm.pdf.
- Segui, M. E., “Predicting a browser’s next online behavior using markov and hidden markov models with preference clustering”, Master’s Thesis, Institute of Mathematics, University of the Philippines, Diliman (2023).
References
Awad, M. and Khanna, R., “Efficient learning machines: theories, concepts, and applications for engineers and system designers”, Springer nature, (2015).
Bernardino, T. T. and Santos, J.M., “Markov chain representation of individual and group lending in microcredit”, AIP Conference Proceedings 2192(1) (2019), 060004-1 - 060004-13. https://doi.org/10.1063/1.5139150.
Diener, F., Diener, M., Khodr, O., and Protter, P., “Mathematical models for microlending”, Proceedings of the 16th Mathematical Conference of the Bangladesh Mathematical Society Volume 1 (2009).
Diener, F. and Khodr, O., “Mathematical models for individual and group lending in microfinance”, Universit´e de Nice, Laboratoire de Math´ematiques (2008), https://math.univ-cotedazur.fr/ diener/Mifi/papierKodrDiener.pdf.
Dulay, S., “Markov chain models of microcredit and the application of the perron-frobenius theorem”, BS Thesis, Institute of Mathematics, University of the Philippines Diliman (2018).
Giampieri, G., Davis, M., and Crowder, M. “Analysis of default data using hidden Markov models”, Quantitative Finance, 5(1) (2005), 27–34. https://doi.org/10.1080/14697680500039951
Frazzoli, E., “Principles of Autonomy and Decision Making”, University Lecture, Massachusetts Institute of Technology (2010).
Giva, M.A., “Hidden markov representation of microcredit”, BS Thesis, Institute of Mathematics, University of the Philippines, Diliman (2023).
Hassan, R., and Nath, B., “Stock market forecasting using hidden Markov model: A new approach”, Proceedings of the 2005 5th International Conference on Intelligent Systems Design and Applications (2003).
Jurafsky, D. and Martin, J., “Speech and language processing”, https://web.stanford.edu/ jurafsky/slp3/A.pdf, Accessed: 03-05-2023.
Kamath, H. and Jahan, N. F., “Using hidden markov model to monitor possible loan defaults in banks”, International Journal of Economics & Business Administration Vol. 0(4) (2020), 1097-1107.
Li, N., “Hidden markov model and financial application” Master’s thesis, The University of Texas at Austin (2016).
Ntwiga, D.B., Ogutu, C., and Kirumbu, M.K., “Inclusion of peer group and individual low-income earners in m-shwari micro-credit lending: a hidden markov model approach”, International Journal of Electronic Finance 9(2) (2018), 121-133.
Ntwiga, D.B., Ogutu, C., Kirumbu, M.K., and Weke, P., “A Hidden Markov Model of Risk Classification among the Low Income Earners”, Journal of Finance and Economics, 6(6) (2018), 242-249. https://doi.org/10.12691/jfe-6-6-6
Ntwiga, D.B. and Weke, P., “Credit Scoring for M-Shwari using Hidden Markov Model”, European Scientific Journal, ESJ, 12(15) (2016), 176. https://doi.org/10.19044/esj.2016.v12n15p176
Rabiner, L., “A tutorial on hidden markov models and selected applications in speech recognition” Proceedings of the IEEE 77(2) (1989), 257–286.
Ramage, D., “Hidden markov models fundamentals”, CS229 Section Notes (2007), https://cs229.stanford.edu/section/cs229-hmm.pdf.
Segui, M. E., “Predicting a browser’s next online behavior using markov and hidden markov models with preference clustering”, Master’s Thesis, Institute of Mathematics, University of the Philippines, Diliman (2023).