MATHEMATICAL MODELS FOR MICROLENDING

MATHEMATICAL MODELS FOR MICROLENDING Francine Diener ? Marc Diener ? Osman Khodr ? Philip Protter † Proceedings of the 16th Mathematical Conference of Bangladesh Mathematical Society 17-19 December, 2009, Dhaka, Bangladesh Abstract Microlending has not yet been placed on a firm mathematical foundation, in contrast to the highly developed theory of Mathematical Finance. Here we propose a first step, modeling a slightly simplified procedure than the one actually used, as a Markov chain. Using this model we compute the expected benefit each borrower gains from his or her activity. We compute the distribution of the beneficiaries among the population involved, and discuss the resultant equilibrium, as well as the issue of strategic defaults. Our proposed model builds on the pioneering work of 2006, by G.A. Tedeschi. 1 Introduction The mathematical formulation of microcredit is in its infancy, in stark contrast to the highly developed theory of Asset Pricing, and even of Credit Risk. We take a first step here, by proposing a Markov chain model to formalize the dynamic model of microcredit lending. In doing so, we recover some of the basic results and formulas of G.A. Tedeschi [3] , who obtained them through economic reasoning alone. Our model leads naturally to an optimization problem which is for the lender to choose the optimal time of exclusion with regards to a given borrower.has nothing bangladesh mathematical rational risk-neutral simplified model markov chain probability ? microcredit loan can dynamic distribution pi? been shown