Group Survival Probability under Contagion in Microlending

In the context of micro-finance, a group of individuals undertake business projects that may interfere with one another. A contagious default happens if one person's project failure leads to the default of another group member. In this paper, we apply a probabilistic approach to analyze the impact of such contagion among investment group members. Firstly, a general formula is provided to compute the group survival probability with the presence of contagion effect. Then, special cases of this probability model are examined in detail. 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. This differs from the non-contagious scenario, where the default probability decreases monotonically with respect to the group size. Afterwards, we provide an upper bound of the optimal group size under the homogeneous setup; so, one can run a linear search within finite time to locate this optimizer.