We construct a recommendation system for car insurance, to allow agents to optimize up-selling performances, by selecting customers who are most likely to subscribe an additional cover. The originality of our recommendation system is to be suited for the insurance context. While traditional recommendation systems, designed for online platforms (e.g. e-commerce, videos), are constructed on huge datasets and aim to suggest the next best offer, insurance products have specific properties which imply that we must adopt a different approach. Our recommendation system combines the XGBoost algorithm and the Apriori algorithm to choose which customer should be recommended and which cover to recommend, respectively. It has been tested in a pilot phase of around 150 recommendations, which shows that the approach outperforms standard results for similar up-selling campaigns. Recommendation system Up-selling Car insurance XGBoost algorithm Apriori algorithm

Hawkes processes are temporal self-exciting point processes. They are well established in earthquake modelling or finance and their application is spreading to diverse areas. Most models from the literature have two major drawbacks regarding their potential application to insurance. First, they use an exponentially-decaying form of excitation, which does not allow a delay between the occurrence of an event and its excitation effect on the process and does not fit well on insurance data consequently. Second, theoretical results developed from these models are valid only when time of observation tends to infinity, whereas the time horizon for an insurance use case is of several months or years. In this paper, we define a complete framework of Hawkes processes with a Gamma density excitation function (i.e. estimation, simulation, goodness-of-fit) instead of an exponential-decaying function and we demonstrate some mathematical properties (i.e. expectation, variance) about the transient regime of the process. We illustrate our results with real insurance data about natural disasters in Luxembourg.