Assicurazioni salute e analisi di sopravvivenza: un'applicazione al caso italiano

This thesis stems from my strong interest in reconciling a theoretical and statistical subject with an important aspect of people's social life. I have therefore decided to address the issue of people's health, which is a fundamental aspect of everyone's life. This is linked to the fundamental right to health which the Italian Constitution, through Article 32, guarantees to all citizens. Thus, in the first chapter, the national health system and health expenditure are presented, which are addressed both publicly by the state and by households privately. Precisely because of the strong growth in private health expenditure, the role that health insurance can play in the near future to mitigate the burden of private expenditure on households is important. The main types of health insurance in the market will be presented in Chapter 2. At this point, it is important to understand at the actuarial level what are some characteristics that distinguish the types of policy described above. This is the objective of Chapter 3, which presents an actuarial model useful for modelling the various types of health insurance. The next chapters, Chapter 4 and 5 present statistical and econometric methods to determine the probabilities of the status changes between the nodes of the actuarial model presented in Chapter 3. These methods belong to the theory of survival and serve precisely to understand what the future development of the demographic sample will be in terms of survival and death probability. Chapter 6 also presents methodologies for reading and understanding the results obtained through the statistical and econometric methods presented above. Finally, in Chapter 7, we come to reconcile the theoretical aspect of survival analysis with the social aspect of health insurance. Thus, a Cox regression is applied to a database that seeks to be likely a pool for a policy that guarantees an annuity in the event of permanent invalidity from injury. There are also appendices dealing with mathematical and statistical issues not discussed in the main corpus of the dissertation, so as not to burden the reading of the same, but which can be useful to the reader to better understand the topics covered in the thesis. In conclusion, there is a chapter that presents the Matlab code used both for creating the images present in the thesis and for carring out the Cox regression present in the application chapter.