This thesis contributes a structured inquiry into the open actuarial mathematics problem of modelling user behaviour using machine learning methods, in order to predict purchase intent of non-life insurance products. It is valuable for a company to understand user interactions with their website as it provides rich and individualized insight into consumer behaviour. Most of existing research in user behaviour modelling aims to explain or predict clicks on a search engine result page or to estimate click-through rate in sponsored search. These models are based on concepts about users' examination patterns of a web page and the web page's representation of items. Investigating the problem of modelling user behaviour to predict purchase intent on a business website, we observe that a user's intention yields high dependency on how the user navigates the website in terms of how many different web pages the user visited, what kind of web pages the user interacted with, and how much time the user spent on each web page. Inspired by these findings, we propose two different ways of representing features of a user session leading to two models for user click-based purchase prediction: one based on a Feed Forward Neural Network, and another based on a Recurrent Neural Network. We examine the discriminativeness of user-clicks for predicting purchase intent by comparing the above two models with a model using demographic features of the user. Our experimental results show that our click-based models significantly outperform the demographic model, in terms of standard classification evaluation metrics, and that a model based on a sequential representation of user clicks yields slightly greater performance than a model based on feature engineering of clicks.