The infinite-horizon investment-consumption problem for Epstein-Zin stochastic differential utility. I: Foundations



Herdegen, Martin, Hobson, David and Jerome, Joseph ORCID: 0000-0002-8312-0053
(2022) The infinite-horizon investment-consumption problem for Epstein-Zin stochastic differential utility. I: Foundations. FINANCE AND STOCHASTICS, 27 (1). pp. 127-158.

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Abstract

<jats:title>Abstract</jats:title><jats:p>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.</jats:p>

Item Type: Article
Uncontrolled Keywords: Epstein-Zin stochastic differential utility, Lifetime investment and consumption, Backward stochastic differential equations, Discounted aggregator
Divisions: Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User: Symplectic Admin
Date Deposited: 14 Mar 2022 17:05
Last Modified: 18 Jan 2023 21:10
DOI: 10.1007/s00780-022-00495-6
Open Access URL: https://arxiv.org/abs/2107.06593
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3150777