A Markovian approach to the analysis and optimization of a portfolio of credit card accounts

Abstract

This thesis introduces a novel approach to the analysis and control ofa portfolio of credit card accounts, based on a two dimensional MarkovDecision Process (MDP). The state variables consist of the due statusof the account and its unused credit limit. The reward function is thoroughlydetailed to feature the specificities of the card industry. Theobjective is to find a collection policy that optimizes the profit of thecard issuer. Sample MDPs are derived by approximating the transitionprobabilities via a dynamic program. In this approximation, the transitionsare governed by the current states of the account, the monthlycard usages and the stochastic repayments made by the cardholder. Acharacterization of the cardholdersa?? rationality is proposed. Various rationalprofiles are then defined to generate reasonable repayments. Theensuing simulation results re-affirm the rationality of some of the currentindustrial practices. Two extensions are finally investigated. Firstly, avariance-penalized MDP is formulated to account for risk sensitivity indecision making. The need for a trade-off between the expected rewardand the variability of the process is illustrated on a sample problem.Secondly, the MDP is transformed to embody the attrition phenomenonand the bankruptcy filings. The subsequent simulation studies tally withtwo industrial recommendations to retain cardholders and minimize baddebt losses.