Estendere il modello Lee-Carter con Neural Networks

In the field of mortality rates forecasting, the Lee–Carter model (1992) is considered as the benchmark among stochastic models. Thanks to its simplicity and robustness, it is still a widely used and valid model, despite not being as modern or elaborate as other alternatives. In this thesis we are going to extend this model using Machine Learning techniques, in particular Neural Networks. While lacking in interpretability, Neural Networks can achieve a much higher predictive power than classical methods and therefore have attracted the interest of many researches. We will discuss the inherent pros and cons of Neural Networks, with a focus on the issues and possible pitfalls faced when applying them to actuarial modelling. Furthermore, we will implement our own model: a Long Short-Term Memory, i.e. a particular type of Recurrent Neural Network. We will compare it to state-of-the-art models developed by researchers and discuss its performance relative to them.\\ The thesis is structured as follows: - First we will introduce the field of mortality modelling and briefly review the literature on the subject, with a particular interest in the application of Machine Learning techniques in the area. - In the second chapter, after setting the notation and the basic definitions, we will move on to the Lee-Carter model itself: its description ,the parameters estimation and the most relevant extensions. - In the third chapter we will introduce Neural Networks. Starting from the most simple examples, we will describe their structure and examine their modelling and fitting details, in order to give a broad overview of the subject. We will then briefly introduce Recurrent Neural Networks and Long Short-Term Memory and discuss the design of Neural Networks and their application to actuarial modelling. - In the fourth chapter we will develop our own Neural Network and train it on the Italian dataset for mortality data: after exploring briefly the data and describing the implementation, we will compare its performance with respect to other Neural Networks. - Conclusions are drawn in the fifth chapter: we discuss the most important aspects of moving from traditional actuarial modelling to Machine Learning and propose some future research topics.