Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities
We study existence, uniqueness and stability of solutions for a class of discrete time recursive utilities models. By combining two streams of the recent literature on recursive preferences - one that analyzes principal eigenvalues of valuation operators and another that exploits the theory of monotone concave operators - we obtain conditions that are both necessary and sufficient for existence and uniqueness. We also show that the natural iterative algorithm is convergent if and only if a solution exists. Consumption processes are allowed to be nonstationary.
The authors thank Anmol Bhandari, Tim Christensen, Ippei Fujiwara, Jinill Kim, Daisuke Oyama, and Guanlong Ren for helpful comments. Financial support from ARC grant FT160100423 is gratefully acknowledged. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
JAROSLAV BOROVIČKA & JOHN STACHURSKI, 2020. "Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities," The Journal of Finance, vol 75(3), pages 1457-1493. citation courtesy of