Modèles de dépendance hiérarchique pour l'évaluation des passifs et la tarification en actuariat

Authors: Abdallah, Anas
Advisor: Cossette, HélèneBoucher, Jean-Philippe
Abstract: The objective of this thesis is to propose innovative hierarchical approaches to model dependence within and between risks in non-life insurance in general, and in a loss reserving context in particular. One of the most critical problems in property/casualty insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. However, most risks are related to each other in practice, and this correlation needs to be taken into account. Recently, Shi and Frees (2011) proposed to include dependence between lines of business in a pairwise manner, through a copula that captures dependence between two equivalent cells of two different runoff triangles. In this thesis, we propose to generalize this model with two different approaches. Firstly, by using hierarchical Archimedean copulas to accommodate correlation within and between lines of business, and secondly by capturing this dependence through random effects. The first approach will be presented in chapters 2 and 3. In chapter 2, we use partially nested Archimedean copulas to capture dependence within and between two lines of business, through calendar year effects. In chapter 3, we use fully nested Archimedean copulas, to accommodate dependence between more than two lines of business. A copula-based risk aggregation model is also proposed to accommodate dependence. The inference for the dependence structure is performed with a rank-based methodology to bring more robustness to the estimation. In chapter 4, we introduce the Sarmanov family of bivariate distributions to a loss reserving context, and show that its flexibility proves to be very useful for modeling dependence between loss triangles. This dependence is captured by random effects, through calendar years, accident years or development periods. Closed-form expressions are given, and a real life illustration is shown again. In chapter 5, we use the Sarmanov family of bivariate distributions in a dynamic framework, where the random effects are considered evolutionary and evolve over time, to update the information and allow more weight to more recent claims. Hence, we propose an innovative way to jointly model the dependence between risks and over time with an illustration in a ratemaking context. Finally, a brief conclusion recalls the main contributions of this thesis and provides insights into future research and possible extensions to the proposed works.
Document Type: Thèse de doctorat
Issue Date: 2016
Open Access Date: 24 April 2018
Grantor: Université Laval
Collection:Thèses et mémoires

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