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European Journal of Operational Research 212 (2011) 123–130

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European Journal of Operational Research

journal homepage: www.elsevier.com/locate/ejor

Stochastics and Statistics

Modelling the profitability of credit cards by Markov decision processes

Meko M.C. So ⇑, Lyn C. Thomas

School of Management, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom

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This paper derives a Markov decision process model for the profitability of credit cards, which allows lenders to find an optimal dynamic credit limit policy. The states of the system are based on the borrower’s behavioural score and the decisions are what credit limit to give the borrower each period. In determining which Markov chain best describes the borrower’s performance, second order as well as first order Markov chains are considered and estimation procedures developed that deal with the low default levels that may exist in the data. A case study is given in which the optimal credit limit is derived and the results compared with the actual outcomes. Ó 2011 Elsevier B.V. All rights reserved.

Article history: Received 20 May 2008 Accepted 14 January 2011 Available online 21 January 2011 Keywords: OR in banking Markov decision process Credit card Behavioural score Profitability Probability of default

1. Introduction Since the advent of credit cards in the 1960s, lenders have used credit scoring, both application and behavioural scoring, to monitor and control default risk. However in the last decade the lenders’ objectives have changed from minimising default rates to maximising profit. Lenders have recognized that operating decisions are crucial in determining how much profit is achieved from a card and this paper focuses on the most important operating policy: The management of the credit limit. Soman and Cheema (2002) conducted a study on the use of credit limit policies in encouraging...