Convex dynamic programming with (bounded) recursive utility

We consider convex dynamic programs with general (bounded) recursive utilities. The Contraction Mapping Theorem fails when the utility aggregator does not obey any discounting property. This failure occurs even with traditional aggregators and certainty equivalent specifications. However, the Bellman operator admits a unique fixed point when an interior policy is feasible. This happens because utility values are unique at interior consumption plans and, when an interior perturbation is feasible, drops in utility values can be avoided.