Recursive utility with unbounded aggregators

A new framework is presented for the study of the existence and uniqueness of solutions to the Koopmans’ equation in the unbounded case, that is based on the contraction mapping approach. In the bounded below case with bounded consumption streams, uniqueness of the solution in the whole class of weak-star continuous utility functions is obtained. When the aggregator is unbounded below and/or consumption streams are unbounded, existence of a weak-star continuous solution is shown, and a simple criterium to check the sufficient conditions for existence is provided.

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