Modelling online credit card usage

Abstract

The aim of this dissertation is to model the spending behavior of credit cardholders, with the idea of classifying legitimate and fraudulent users separately. The utilisation of Markov theory, in particular the Hidden Markov Model (HMM), was a valuable tool in providing solutions to the three main problems tackled. Dynamic Programming methods were essential in order to reduce the demanding computation of several calculations. Particularly, the Viterbi algorithm was exploited in the second HMM problem known as the Decoding Problem. Theory from Maximum Likelihood was also used especially in the third HMM problem, usually termed as the Learning Problem. A famous Expectation-Maximisation (EM) algorithm called the Baum-Welch algorithm was used so as to obtain the most likely parameters that best describe each credit cardholder's spending patterns. Finally, classification of legitimate and fraudulent users was carried out using cluster analysis.