Theoretical and operational tools adapted to the context of life insurance in French-speaking sub-Saharan Africa: analysis and measurement of mortality-related risks.

Summary In a life insurance market in French-speaking sub-Saharan Africa that is lagging behind but has a bright future if endogenous technical and commercial solutions emerge, the thesis proposes theoretical and operational tools adapted to its development. This approach is in line with the actions undertaken by the regional supervisory authority (CIMA) to provide the region's insurers with appropriate tools. Indeed, CIMA has initiated work on the construction of new regulatory experience tables, which has provided reliable and relevant references for the mortality of the insured population in the region. However, some useful technical issues were not developed in this construction work. The thesis therefore gives them special attention. Thus, on the one hand, the thesis provides tools to account for differences in mortality between countries in the region, while limiting the systematic risks associated with sampling fluctuations (due to small data sample sizes per country). In particular, it appears that if independent modeling of each country is not appropriate, heterogeneity models with observable factors, such as the Cox or Lin and Ying model, can achieve this goal. However, it should be noted that these heterogeneity models do not eliminate the systematic risk of sampling fluctuations in the estimation of the model, but only reduce this risk while increasing the systematic risk of model selection. On the other hand, the thesis also provides tools to model future experience mortality in the region. In the absence of data on past trends in experience mortality, neither the classical Lee-Carter model nor its extensions are applicable. A solution based on a parametric adjustment, an assumption on the shape of the evolution of the mortality level (linear or exponential evolution) and an expert opinion on the generational life expectancy at a given age is then proposed (this work is based on the Bongaarts model). Then, in a second step, assuming the availability of data on past trends (which for the record is not the case at this stage in the region, but should be in the next few years), the thesis proposes a modeling of future mortality from an external mortality reference and an analysis of the associated systematic risks (risks related to sampling fluctuations and the choice of the mortality reference)