Modelling the profitability of credit cards by Markov decision process

This paper derives a model for the profitability of credit cards, which allow lenders to find the optimal dynamic credit limit policy. The model is a Markov decision process, where 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 the Markov chain which best describes the borrower’s performance second order as well as first order Markov chains are considered and estimation procedures that deal with the low default levels that may exist in the data are considered. A case study is used to show how the optimal credit limit can be derived.