Group Survival Probability under Contagion in Microlending

In this paper we apply a probabilistic approach to analyze the impact of contagious default among investment group members. A general formula is given to compute the group survival probability with the presence of contagion effect. Special cases of this probability model are examined. In particular, we show that if the investment group is homogeneous, defined in the paper, then including more members into the group will eventually lead to default with probability 1, contrasting with the non-contagious scenario, where the default probability increases monotonically with respect to the group size. Also, we provide an upper bound of the optimal group size under the homogeneous setup; so, one can run a linear search with finite time to locate this optimizer.