Recursive utility and optimal growth with bounded or unbounded returns

Cuong Le Van (1) , Yiannis Vailakis (2)

1 CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique
2 UCL IRES - Institut de recherches économiques et sociales

In this paper, we propose a unifying approach to the study of recursive economic problems. Postulating an aggregator function as the fundamental expression of tastes, we explore conditions under which a utility function can be constructed. We also modify the usual dynamic programming arguments to include this class of models. We show that Bellman's equation still holds, so many results known for the additively separable case can be generalized for this general description of preferences. Our approach is general, allowing for both bounded and unbounded returns. Many recursive economic models studied in the literature are particular cases of our setting.

Mots clés: Recursive utility; dynamic programming; Bellman equation; unbounded returns

Domaines: Economies et finances; Analyse classique [math.CA]; Optimisation et contrôle [math.OC]

Cuong Le Van, Yiannis Vailakis. Recursive utility and optimal growth with bounded or unbounded returns. Journal of Economic Theory, 2005, 123 (2), pp.187-209. ⟨10.1016/j.jet.2004.06.007⟩. ⟨halshs-00101201⟩