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 pofit 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-classication, 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 dierent 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 dierent during the sampling period. Based on these empirical ndings, 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 ndings show the impact of economy are signicantly 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.

Data Envelopment Analysis (DEA) is a linear programming technique for measuring the relative efficiencies of a set of Decision Making Units (DMUs). Each DMU uses the same set of inputs in differing amounts to produce the same set of outputs in differing quantities. Weights are freely allocated in order to allow these multiple incommensurate inputs and outputs to be reduced to a single measure of input and a single measure of output. A relative efficiency score of a DMU under Constant Returns to Scale is given by maximising the sum of its weighted outputs to the sum of its weighted inputs, such that this ratio can not exceed I for any DMU; with the weights derived from the model being taken to represent the value attributed to the inputs and outputs of the assessment. It is well known in DEA that this free allocation of weights can lead to several problems in the analysis. Firstly inputs and outputs can be virtually ignored in the assessment; secondly any relative relationships between the inputs or outputs can be ignored, and thirdly any relationships between the inputs and outputs can be violated. To avoid/overcome these problems, the Decision Maker's (DM) value judgments are incorporated into the assessment. At present there is one main avenue for the inclusion of values, that of weights restrictions, whereby the size of the weights are explicitly restricted. Thus to include the relative value of the inputs or outputs, the relative value of the weights for these related inputs or outputs are restricted. The popularity of this approach is mainly due to its simplicity and ease of use. The aim of this thesis is, therefore, firstly, to demonstrate that, although the weights restrictions approach is appropriate for many DMs, for a variety of reasons some DMs, may prefer an alternative form for the expression of their values, e.g. so that they can include local values in the assessment. With this in mind, the second aim of this thesis is to present a possible alternative approach for the DMs to incorporate their values in a DEA assessment and, thirdly, it aims to utilise this alternative approach to improve envelopment. This alternative approach was derived by considering the basic concept of DEA, which is that it relies solely on observed data to form the Production Possibility Set (PPS), and then uses the frontier of this PPS to derive a relative efficiency score for each DMU. It could be perceived, therefore, that the reason for DMUs receiving inappropriate relative efficiency scores is due to the lack of suitable DEA-efficient comparator DMIUs. Thus, the proposed approach attempts to estimate suitable input output levels for these missing DEA-efficient comparator DMUs, i.e. Unobserved DMUs. These Unobserved DMUs are based on the manipulation of observed input output levels of specific DEA-efficient DMUs. The aim of the use of these Unobserved DMUs is to improve envelopment, and the specific DEA-efficient DMTJs that are selected as a basis for the Unobserved DMILTs are those that delineate the DEA-efficient frontier from the DEA-inefficient frontier. So, the proposed approach attempts to extend the observed PPS, while assuming that the values of the observed DEA-efficient DMIJs are in line with the perceived views of the DM. The approach was successfully applied to a set of UK bank branches. To illustrate that no approach is all-purpose, and that each has its strengths and weaknesses and, therefore, its own areas of application, a brief comparison is made between the approach of weights restrictions and the approach proposed in this thesis. This thesis is divided into three sections: A - Overview of the research area; B - An alternative perspective for incorporating values in DEA; C - The use of UDMUs to express the DM's values to improve envelopment