#### Predicting the Movement of Individuals in a Multi-state Process Using a Hazard Rate Model

*Written by: Lotte Harrijvan*

During my time at Notilyze I developed a quantitative model for one of their biggest clients as part of my thesis for the master Quantitative Finance. The aim of the project was to map the movement of individuals in a multi-state process consisting of a number of states. Using these movements we can forecast future cash flow. The idea is to use survival analysis to predict the hazards of transitioning in this process. By estimating the hazard or risk to transition to another state, we can predict the future path of an individual in this multi-state process. The hazard of transitioning can be estimated with a Cox regression, which allows us to incorporate individual variables that may affect the transitions. It therefore allows us to estimate the hazards on a monthly base for each individual separately. These hazards are then transformed into transition probabilities. We put these estimated transition probabilities into transition matrices. With these monthly transition matrices we can predict the future path of the individual and produce a state variable over time. This state variable is a dummy variable indicating the active state of the individual.

Next, we use these state variables to predict the monthly payments of an individual because these payments are dependent on the states and this way I was able to link the thesis to a financial concept. A logistic regression is used for these payment predictions with the state variables serving as explanatory variables. Ultimately, the process produces a monthly overview of the individuals distributed over the different states (see figure) together with the monthly payment predictions for each individual. This provides the client with a lot of insights into their core process and it therefore can help them in their decision making. The next step, in finishing my graduate internship at Notilyze, is to implement the model. I will be doing this in cooperation with the client. I am very excited to see my model actually being implemented and used.