This paper introduces a dynamic model of the stochastic repayment behavior exhibited by delinquent credit-card accounts. Based on this model, we construct a dynamic collectability score (DCS) which estimates the account-specific probability of collecting a given portion of the outstanding debt over any given time horizon. The model integrates a variety of information sources, including historical repayment data, account-specific, and time-varying macroeconomic covariates, as well as scheduled account-treatment actions. Two model-identification methods are examined, based on maximum-likelihood estimation and the generalized method of moments. The latter allows for an operational-statistics approach, combining model estimation and performance optimization by tailoring the estimation error to business-relevant loss functions. The DCS framework is applied to a large set of account-level repayment data. The improvements in classification and prediction performance compared to standard bank-internal scoring methods are found to be significant.