Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities

Jaroslav Borovička and John Stachurski

Journal of Finance, 2020, vol. 75, issue 3, 1457-1493

Abstract: We obtain exact necessary and sufficient conditions for existence and uniqueness of solutions of a class of homothetic recursive utility models postulated by Epstein and Zin. The conditions center on a single test value with a natural economic interpretation. The test sheds light on the relationship between valuation of cash flows, impatience, risk adjustment, and intertemporal substitution of consumption. We propose two methods to compute the test value when an analytical solution is not available. We further provide several applications.

Date: 2020
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https://doi.org/10.1111/jofi.12877

Related works:
Working Paper: Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities (2019)
Working Paper: Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities (2018)
Working Paper: Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities (2017)
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