Predicting the Debtor Paths in a Multi-state Process Using a Hazard Rate Model

Abstract In this thesis, we aim to give more insights into the debt collecting process of a collection agency. We perform an in-depth analysis of the path prediction of debtors in this process and provide monthly predictions of their corresponding payments over the next five years. The transitions in this multi-state process are governed by a Markov process and are modeled using a combination of time-to-event models. First, we fit separate intensities to all permitted transitions according to the semi-parametric Cox proportional hazards regression. The impact of fixed individual covariates on the hazard ratio, such as the age of debt and the outstanding amount, are discussed in the duration-independent model. Additionally, the duration-dependent model also discusses the impact of a variable that accumulates the durations in previous states. It turns out that this duration-dependent variable improves the model performance, and we use this model to obtain the transition intensities. Secondly, the individual transition probabilities are estimated with the Aalen-Johansen estimator and put together in monthly transition matrices. These are then used to obtain predictions of the debtor-state variables, indicating the active state of the debtor in each month of our 5-year forecast horizon. Finally, to predict the payments, we use the debtor-state variables as explanatory variables in the linear and logistic regression. It appears that the logistic regression slightly outperforms the linear regression. However, both regressions suggest that the debtor-state variables are very informative predictors. The results show that most payments will be collected within the first year of our 5-year forecast horizon with an average payment rate of 0.11.