Bio-Age-Shifting for dynamical evaluation of demografic risk in a live policies portfolio

This paper presents a model for evaluating the demographic risk in a life policies portfolio. The actuaries usually face the longevity risk by means of projected mortality tables obtained considering the development of the mortality trend. Moreover, the choice of mortality rates with a given projection level is uncertain, and such uncertainty jeopardises the model quality with a so called “projection risk” [2]. In this paper we propose a methodology able to dynamically control the longevity risk component connected to the biological risk. Our proposal consists in considering the correction due to the actual biological risk by using a technique similar to the Age-shifting that we call Bio-Age-Shifting. In order to reach this goal two explicit forms are proposed, the first is multiplicative whether the second is additive. This technique applies to n periodic contract revisions the biological age instead of the chronological age. After the model description some numerical examples illustrate the results, showing the behaviour of the biological risk and its effects on the adjustments of mortality tables and consequently on fees and benefits. The model is applicable to life and Long Term Care policies but also to the social security sector.