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The infinite horizon investment-consumption problem for Epstein-Zin stochastic differential utility. I : Foundations
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Herdegen, Martin, Hobson, David G. and Jerome, Joseph (2023) The infinite horizon investment-consumption problem for Epstein-Zin stochastic differential utility. I : Foundations. Finance and Stochastics, 27 . pp. 127-158. doi:10.1007/s00780-022-00495-6 ISSN 0949-2984.
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Official URL: https://doi.org/10.1007/s00780-022-00495-6
Abstract
The goal of this article is to provide a detailed introduction to infinite-horizon investment–consumption problems for agents with preferences described by Epstein–Zin (EZ) stochastic differential utility (SDU). In the setting of a Black–Scholes–Merton market, we seek to describe all parameter combinations that lead to a well-founded problem in the sense that the problem is not just mathematically well posed, but the solution is also economically meaningful. The key idea is to consider a novel and slightly different description of EZ SDU under which the aggregator has only one sign. This new formulation clearly highlights the necessity for the coefficients of relative risk aversion and of elasticity of intertemporal complementarity (the reciprocal of the coefficient of intertemporal substitution) to lie on the same side of unity.
Item Type: | Journal Article | ||||||||
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Subjects: | H Social Sciences > HB Economic Theory H Social Sciences > HG Finance Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Differential games, Stochastic integral equations , Utility theory -- Mathematical models, Portfolio management -- Mathematical models, Stochastic control theory | ||||||||
Journal or Publication Title: | Finance and Stochastics | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0949-2984 | ||||||||
Official Date: | January 2023 | ||||||||
Dates: |
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Volume: | 27 | ||||||||
Page Range: | pp. 127-158 | ||||||||
DOI: | 10.1007/s00780-022-00495-6 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 12 October 2022 | ||||||||
Date of first compliant Open Access: | 12 October 2022 | ||||||||
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