Calculating optimal limits for transacting credit card customers

TL;DR

This paper develops a model to determine optimal credit limits for credit card customers, using stochastic processes and balance control policies, with practical application to real purchase data.

Contribution

It introduces a novel stochastic model for calculating optimal credit limits considering purchase processes and balance controls, connecting to the newsvendor model.

Findings

Optimal limits scale with purchase distribution

Probability of exceeding limit remains constant

Model applied successfully to real data

Abstract

We present a model of credit card profitability, assuming that the card-holder always pays the full outstanding balance. The motivation for the model is to calculate an optimal credit limit, which requires an expression for the expected outstanding balance. We derive its Laplace transform, assuming that purchases are made according to a marked point process and that there is a simplified balance control policy in place to prevent the credit limit being exceeded. We calculate optimal limits for a compound Poisson process example and show that the optimal limit scales with the distribution of the purchasing process and that the probability of exceeding the optimal limit remains constant. We establish a connection with the classic newsvendor model and use this to calculate bounds on the optimal limit for a more complicated balance control policy. Finally, we apply our model to real credit card purchase data.