Epstein-Zin Stochastic Differential Utility: Existence, Uniqueness, Concavity, and Utility Gradients

24 Pages Posted: 3 Jul 2015 Last revised: 1 Jun 2016

See all articles by Thomas Seiferling

Thomas Seiferling

University of Kaiserslautern - Department of Mathematics

Frank Thomas Seifried

University of Trier

Date Written: May 23, 2016

Abstract

In a fully general semimartingale setting, this article establishes existence, uniqueness, monotonicity, concavity, and a utility gradient inequality for continuous-time recursive utility in the Epstein-Zin parametrization with relative risk aversion $\gamma$ and elasticity of intertemporal substitution $\psi$ such that either $\gamma\psi,\psi\geq 1$ or $\gamma\psi,\psi\leq 1$.

Keywords: recursive utility, stochastic differential utility, utility gradient, BSDEs

JEL Classification: D81, D90, G12

Suggested Citation

Seiferling, Thomas and Seifried, Frank Thomas, Epstein-Zin Stochastic Differential Utility: Existence, Uniqueness, Concavity, and Utility Gradients (May 23, 2016). Available at SSRN: https://ssrn.com/abstract=2625800 or http://dx.doi.org/10.2139/ssrn.2625800

Thomas Seiferling

University of Kaiserslautern - Department of Mathematics ( email )

D-67653 Kaiserslautern
Germany

Frank Thomas Seifried (Contact Author)

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

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