The Infinite Horizon Investment-Consumption Problem for Epstein-Zin Stochastic Differential Utility

41 Pages Posted: 16 Jul 2021

See all articles by Joseph Jerome

Joseph Jerome

University of Warwick - Department of Statistics

Martin Herdegen

University of Warwick - Department of Statistics

David Hobson

University of Warwick

Date Written: July 14, 2021

Abstract

In this article, we consider the optimal investment-consumption problem for an agent with preferences governed by Epstein-Zin stochastic differential utility who invests in a constant-parameter Black-Scholes-Merton market.

The paper has three main goals: first, to provide a detailed introduction to infinite-horizon Epstein-Zin stochastic differential utility, including a discussion of which parameter combinations lead to a well-formulated problem; second, to prove existence and uniqueness of infinite horizon Epstein-Zin stochastic differential utility under a restriction on the parameters governing the agent's risk aversion and temporal variance aversion; and third, to provide a verification argument for the candidate optimal solution to the investment-consumption problem among all admissible consumption streams.

To achieve these goals, we introduce a slightly different formulation of Epstein-Zin stochastic differential utility to that which is traditionally used in the literature. This formulation highlights the necessity and appropriateness of certain restrictions on the parameters governing the stochastic differential utility function.

Keywords: Epstein--Zin stochastic differential utility, lifetime investment and consumption, backward stochastic differential equations, optional strong supermartingales.

JEL Classification: C61, G11

Suggested Citation

Jerome, Joseph and Herdegen, Martin and Hobson, David, The Infinite Horizon Investment-Consumption Problem for Epstein-Zin Stochastic Differential Utility (July 14, 2021). Available at SSRN: https://ssrn.com/abstract=3886439

Joseph Jerome (Contact Author)

University of Warwick - Department of Statistics ( email )

Coventry, CV47AL
United Kingdom

HOME PAGE: http://https://warwick.ac.uk/fac/sci/statistics/staff/research_students/jerome/

Martin Herdegen

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

David Hobson

University of Warwick ( email )

CV4 7AL
United Kingdom

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