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) that 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. This paper was accepted by Noah Gans, stochastic models and simulation.
Based on a dynamic model of the stochastic repayment behavior exhibited by delinquent credit-card accounts in the form of a self-exciting point process, a bank can control the arrival intensity of repayments using costly account-treatment actions. A semianalytic solution to the corresponding stochastic optimal control problem is obtained using a recursive approach. For a linear cost of treatment effort, the optimal policy in the two-dimensional (intensity, balance) space is described by the frontier of a convex action region. The unique optimal policy significantly reduces a bank's loss given default and concentrates the collection effort onto the best possible actions at the best possible times so as to minimize the sum of the expected discounted outstanding balance and the discounted cost of the collection effort, thus maximizing the net value of any given delinquent credit-card account.
We argue that dynamic pricing motivated by the management of inventory holding and ordering costs leads to increased operational efficiencies that could benefit firms without hurting consumers. To demonstrate this point, we equip the traditional economic order quantity (EOQ) setting with a rich set of demand models and compare social outcomes under two alternatives, dynamic and static pricing. We show that dynamic pricing generates higher retailer profits, a lower average price per unit sold, and higher sales volumes than static pricing. The mechanism behind the result is that with dynamic pricing the retailer ties the price of each unit to its holding costs, which allows him to increase the order quantity compared with static pricing and thus save on fixed ordering costs. Some of these cost savings are passed to consumers. Moreover, we demonstrate that this mechanism is robust to the presence of price-anticipating (strategic) consumer behavior. This paper was accepted by Serguei Netessine, operations management.
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