Epargne privée et retraite par répartition dans un modèle de croissance optimale, en avenir incertain et avec générations d'agents.

[fre] The role of the public pension system in a model of optimal growth with overlapping generations. . Few studies have dealt with optimal growth with uncertain environment and the role of a public pension scheme in optimal growth has not generally been considered. In this paper, we use an overlapping generations model in order to answer the following question : does an optimal rate of contribution exist, i.e a contribution rate maximizing. [eng] The role of the public pension system in a model of optimal growth with overlapping generations. . Few studies have dealt with optimal growth with uncertain environment and the role of a public pension scheme in optimal growth has not generally been considered. In this paper, we use an overlapping generations model in order to answer the following question : does an optimal rate of contribution exist, i.e a contribution rate maximizing social welfare? The answer is yes and the intuition of the result is as follows : according to portfolio theory, agents should hold two risky assets : (i) savings, the return on which is, in our model, the return on physical capital and (ii) "contributions" which give rights to benefits. The model works under the assumption of one source of uncertainty (technological uncertainty) or two sources (technological and demographical). Realistic values of the optimal rate of contribution are obtained, when simulations are run.