Utilisation des estimateurs de kaplan-meier par génération et de hoem pour la construction de tables de mortalité prospectives.

Summary Data quality is an overarching concern when it comes to building a mortality model or prospective mortality tables. This is even more significant when these procedures are based on a small population, as data may show major random fluctuations due to a lack of information for particular ages. Such situations arise frequently with the entry into force of Solvency II as insurers shall consider their own data sets, limited in size, to build best estimate tables. Since parametric methods are too rough to capture a realistic mortality pattern in two dimensions, the mortality profile is quite often adjusted using exogenous information, such as a table based on a national population. In light of this, the aim of this paper is to discuss the problem of choosing appropriate estimators for two-dimensional mortality rates or death rates in the presence of independent censoring. Indeed, practitioners currently use the Hoem estimator or the Kaplan-Meier estimator split by generation without questioning their relevance and reliability. We propose in this paper a comparative analysis of these estimators and try to give some criteria to choose one approach over another, and give some figures based on a real insurance portfolio and simulated data. Finally, we provided some non-parametric estimators for a direct estimation of death rates both with the cohort and the period approaches.