Optimal Consumption and Investment with Epstein-Zin Recursive Utility

SAFE Working Paper No. 52

43 Pages Posted: 4 Jun 2014 Last revised: 6 Jul 2016

See all articles by Holger Kraft

Holger Kraft

Goethe University Frankfurt

Thomas Seiferling

University of Kaiserslautern - Department of Mathematics

Frank Thomas Seifried

University of Trier

Multiple version iconThere are 2 versions of this paper

Date Written: July 4, 2016

Abstract

We study continuous-time optimal consumption and investment with Epstein-Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton-Jacobi-Bellman equation by a fixed point argument and makes it possible to compute both indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.

Keywords: consumption-portfolio choice, asset pricing, stochastic differential utility, incomplete markets, fixed point approach, FBSDE

JEL Classification: G11, G12, D52, D91, C61, C68

Suggested Citation

Kraft, Holger and Seiferling, Thomas and Seifried, Frank Thomas, Optimal Consumption and Investment with Epstein-Zin Recursive Utility (July 4, 2016). SAFE Working Paper No. 52. Available at SSRN: https://ssrn.com/abstract=2444747 or http://dx.doi.org/10.2139/ssrn.2444747

Holger Kraft (Contact Author)

Goethe University Frankfurt ( email )

Faculty of Economics and Business Administration
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany

Thomas Seiferling

University of Kaiserslautern - Department of Mathematics ( email )

D-67653 Kaiserslautern
Germany

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universit├Ątsring 19
Trier, 54296
Germany

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

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