Optimizing credit limit policy by Markov Decision Process Models

Abstract

Credit cards have become an essential product for most consumers. Lenders have recognized the profit that can be achieved from the credit card market and thus they have introduced different credit cards to attract consumers. Thus, the credit card market has undergone keen competition in recent years. Lenders realize their operation decisions are crucial in determining how much profit is achieved from a card. This thesis focuses on the most well-known operating policy: the management of credit limit. Lenders traditionally applied static decision models to manage the credit limit of credit card accounts. A growing number of lenders though want improved models so as to monitor the long-term risk and return of credit card borrowers.
This study aims to use Markov Decision Process, which is a well-developed sequential decision model, to adjust the credit limit of current credit card accounts. The behavioural score, which is the way of assessing credit card holder's default risk in the next year, is used as the key parameter to monitor the risk of every individual account. The model formulation and the corresponding application techniques, such as state coarse-classification, choice of Markovity order, are discussed in this thesis.
One major concern of using Markov Decision Process model is the small sample size in certain states. In general credit card lenders have lots of data. However, there may be no examples in the data of transitions from certain states to default, particularly for those high quality credit card accounts. If one simply uses zero to estimate these states' transition probabilities, this leads to apparent 'structural zeros' states which change the connectedness of the dynamics in the state space. A method is developed in this thesis to overcome such problems in real applications.
The economy and retail credit risk are highly correlated and so one key focus of this study is to look at the interaction between credit card behavioural score migrations and the economy. This study uses different credit card datasets, one from Hong Kong and one from United Kingdom, to examine the impact of economy on the credit card borrowers' behaviour. The economies in these two areas were different during the sampling period. Based on these empirical findings, this study has generalized the use of macroeconomic measurements in the credit limit models. This thesis also proposed segmenting the credit card accounts by the accounts' repayment patterns. The credit card population in general can be segmented into Transactors or Revolvers. Empirical findings show the impact of economy are significantly different for Transactors and Revolvers. This study provides a detailed picture of the application of Markov Decision Process models in adjusting the credit limit of credit card accounts.

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ORCID for Mee Chi So: orcid.org/0000-0002-8507-4222

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