Following population ageing and some recently engaged reforms of pensions systems in several European countries, the question of how to link systems to longevity has become a topic of major interest. Not only longevity is a crucial aspect to take into account in pension reforms but also differential mortality has to be considered. Besides, pension systems have two main objectives; the first one being to provide resources to individuals in their old age, once they are not able to work anymore and the second one being a redistributive concern. Indeed, in the latter case, many European Social Security systems are used by governments as an instrument to smooth inequalities so that low-wage individuals obtain higher replacement rates than high-wage individuals. Yet, recent studies proved that part of this income redistribution is neutralized because, precisely, of differences in life expectancy. To be more explicit, individuals with lower wage get higher replacement rates but also have, on average, a lower life expectancy so that they do not benefit from this redistribution as much as they ought to. Thus, when talking about the link between life expectancy and pension design, several issues have to be considered. On the one hand, one has to consider that increased life expectancy makes more urgent the reform of our systems, since financial viability is at stake but, on the other hand, differential mortality has also to be taken into account in the design of Social Security schemes. Our project will then mainly focus on the issue of the optimal design of Social Security when individuals have different life expectancies and try to answer the following questions: how should differential mortality be included in pension systems? How should contributions and benefits be linked to life duration? This project then lies at the frontier of public economics, health economics, behavioral economics and the economics of ageing.