Etablissement de tables de mortalité relatives au marché belge sur base des statistiques de la BNB

Details

Supervisors

Denuit, Michel

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

enThis Master thesis focuses on the development of mortality tables for the Belgian market based on statistics from the NBB; these tables play a central role in actuarial science, particularly in risk management and insurance applications. The main objective of this work is to highlight the multiple coverage present in the NBB’s mortality statistics, to derive the actual crude mortality rates using the models and methods employed, and finally to produce mortality tables ready for actuarial use. To do this, we first modelled the NBB data under a multi-holding assumption, generated data based on this modelling, and ran our various model functions. We did this without initially taking into account the exact response to be used (initial method). We then proceeded with an iterative method to reconstruct the correct response and verify the stability and convergence of ours results. Ours simulations study yielded fairly relevant and interesting results. This then enabled us to apply the methodology to the NBB data. The study draws on data from the BNB and utilises several models, notably cpglm() and cpglmm() (from the cplm package), as well as Poisson gam() and Tweedie gam() (from the mgcv package). The results of the initial method are compared with crude mortality rates, which is quite interesting; however, actual mortality rates and evidence of multiple detention are not yet included. We therefore proposed an iterative method, which yielded very satisfactory results in terms of convergence and stability, both for the actual mortality rates and for multiple detention. Furthermore, we also obtained a stabilisation of the actual exposures. The results highlight the presence of multi-holdings, with the estimated actual mortality rates aligning with the gross mortality rates (BNB data), and emphasise the importance of selecting appropriate mortality's tables in actuarial practice to avoid under- or over-pricing, for example in life insurance. This work provides useful information for risk assessment and contributes to a better understanding of mortality dynamics in insurance and pension systems.