Paper: arXiv 2509.11579

Authors: Héctor Jasso-Fuentes, Alejandra Quintos, Xinta Yang

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical probability model to establish optimal group size under default contagion in microfinance. However, it is purely theoretical with no empirical data analysis, backtesting, or real-world microlending data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze impact of contagious default on group survival in microlending] --> B[Input Parameters: Group size, individual success rates, contagion probability]
    B --> C[Develop Probabilistic Model for Group Survival Probability]
    C --> D[Analyze Special Case: Homogeneous Investment Groups]
    D --> E[Derive Mathematical Upper Bound for Optimal Group Size]
    E --> F[Key Outcome 1: Larger homogeneous groups lead to default with probability 1]
    E --> G[Key Outcome 2: Optimal group size found via finite linear search]

Cited References (18)

  1. Banker to the Poor (2007)
  2. Rural financial markets in low-income countries: Recent controversies and lessons (1986)
  3. The role of groups and credit cooperatives in rural lending (1990)
  4. Group lending, repayment incentives and social collateral (1995)
  5. The impacts of microfinance: Evidence from joint-liability lending in Mongolia (2015)
  6. Can social cohesion be harnessed to repair market failures? Evidence from group lending in Guatemala (1999)
  7. Peer group micro-lending programs in Canada and the United States (1999)
  8. Mathematical models for microlending (2009)
and 10 more
  1. Randomness of interest rates in microcredit (2016)
  2. The microfinance promise (1999)
  3. Group-lending with sequential financing, contingent renewal and social capital (2007)
  4. The role of group size in group lending (2015)
  5. Optimal group size in joint liability contracts (2017)
  6. Group size and social ties in microfinance institutions (2006)
  7. Infectious defaults (2001)
  8. Contagion in graphons (2023)
  9. On the Lambert W function (1996)
  10. Optimal group size in microlending (2022)

0 of 18 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.