Necessary and Sufficient Conditions for Existence and Uniqueness of Recursive Utilities

• 成果类型: Article
• 署名作者: Borovicka, Jaroslav; Stachurski, John
• 署名单位: Federal Reserve System - USA; Federal Reserve Bank - Minneapolis; Australian National University
• 刊物名称: JOURNAL OF FINANCE
• ISSN/ISSBN: 0022-1082
• DOI: 10.1111/jofi.12877
• 发表日期: 2020
• 页码: 1457-1493
• 关键词: LONG-TERM RISK; RUN RISKS; consumption

摘要

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.