Survival analysis of actuarial data with missing observations

Abstract

Combining information from pension scheme datasets is of fundamental importance in order to obtain more consistent and efficient estimates of mortality rates, which are used when assessing and managing longevity risk. A major problem faced in these type of analysis is given by the case, not uncommon, that pension scheme datasets provide different sets of informations. In this work we develop techniques, based on missing data statistics, which aim at carrying out mortality analysis by making the best use of available information, with particular emphasis on individual socio-economic characteristics. In particular, the stratification of the combined mortality experience is avoided and the information not available for all units therein is not discarded. The techniques of this work are analysed from a three-fold perspective: i) the analysis of the mathematical conditions needed to uniquely identify the probability distribution of interest; ii) the analysis, adaptation and the development of fitting algorithms for tackling the inferential task; and iii) the analysis of the impact of using these techniques for the estimation of demographic and financial quantities of interest for an actuary.