Pricing the Invisible Borrower: An Actuarial Approach to the Design of Dynamic Credit Extension

This working paper proposes a novel application of actuarial credibility theory to the design of dynamic credit extension for borrowers with no credit score and no financial transaction history, a population estimated at 1.3 billion adults worldwide. Building on real data from Home Credit Group (more than 210,000 loans, 13.6 million repayment records, and 3.84 million monthly credit card balances), the paper derives a hierarchical Bayesian risk model, written theta(n,q), that decomposes borrower default risk into a structural floor and an individually reducible component. The model is derived along two independent routes, linear least-squares credibility and the exact Bayes posterior mean (Jewell, 1974), and calibrated against real data with R-squared values of 0.87 and 0.84. This risk model is then integrated into a unified framework spanning contract theory under asymmetric information, behavioral corrections for present-biased borrowers, dynamic programming, and multi-lender market equilibrium, yielding a closed-form, implementable credit limit function suitable for deployment in a secured credit card product. A Monte Carlo validation compares the theoretical optimum against Home Credit's actual lending rule. The result does not support a simple claim that theory outperforms practice. Instead, the paper reframes its closed-form solution as a normative benchmark for evaluating real-world lending rules, and reports this course correction transparently as part of its methodological contribution.