Data Analysis for Insurance: Recommendation System Based on a Multivariate Hawkes Process

The objective of the thesis is to build a recommendation system for insurance. By observing the
behaviour and the evolution of a customer in the insurance context, customers seem to modify
their insurance cover when a significant event happens in their life. In order to take into account
the influence of life events (e.g. marriage, birth, change of job) on the insurance covering selection
from customers, we model the recommendation system with a Multivariate Hawkes Process
(MHP), which includes several specific features aiming to compute relevant recommendations
to customers from a Luxembourgish insurance company.
Several of these features are intent to propose a personalized background intensity for each customer
thanks to a Machine Learning model, to use triggering functions suited for insurance data
or to overcome flaws in real-world data by adding a specific penalization term in the objective
function. We define a complete framework of Multivariate Hawkes Processes with a Gamma
density excitation function (i.e. estimation, simulation, goodness-of-fit) and we demonstrate
some mathematical properties (i.e. expectation, variance) about the transient regime of the
process. Our recommendation system has been back-tested over a full year. Observations from
model parameters and results from this back-test show that taking into account life events by a
Multivariate Hawkes Process allows us to improve significantly the accuracy of recommendations.
The thesis is presented in five chapters. Chapter 1 explains how the background intensity of the
Multivariate Hawkes Process is computed thanks to a Machine Learning algorithm, so that each
customer has a personalized recommendation. Chapter 1 is shown an extended version of the
method presented in [1], in which the method is used to make the algorithm explainable. Chapter
2 presents a Multivariate Hawkes Processes framework in order to compute the dependency
between the propensity to accept a recommendation and the occurrence of life events: definitions,
notations, simulation, estimation, properties, etc. Chapter 3 presents several results of the
recommendation system: estimated parameters of the model, effects of contributions, backtesting
of the model’s accuracy, etc. Chapter 4 presents the implementation of our work into a
R package. Chapter 5 concludes on the contributions and perspectives opened by the thesis.