On the use of multi-state models to measure and manage the risks of an insurance contract.

Summary The implementation of Solvency II leads actuaries to question the good adequacy between models and data. Therefore, this thesis aims to study several statistical approaches, often unknown to practitioners, allowing the use of multi-state methods to model and manage individual risks in insurance. Chapter 1 presents the general context of this thesis and positions its main contributions. We discuss the basic concepts related to the use of multi-state models in insurance and describe the classical inference techniques adapted to the data encountered, whether Markovian or non-Markovian. Finally, we present how these models can be used for credit risk management. Chapter 2 focuses on the use of non-parametric inference methods for the construction of incidence laws in LTC insurance. Since several input causes are likely to be involved and of interest to actuaries, we focus on a method used for estimating continuous-time Markovian multi-state models. We then compare these estimators to those classically used by survival analysis practitioners. This second approach can have significant biases because it does not allow to correctly understand the possible interaction between the causes. In particular, it includes an independence hypothesis that cannot be tested in the context of competing risks models. Our approach then consists in measuring the error made by practitioners when constructing incidence laws. A numerical application is then considered on the basis of data from an insurer With the implementation of the Solvency II framework, actuaries should examine the good adequacy between models and data.