Consumption Investment Optimization with Epstein-Zin Utility in Incomplete Markets

30 Pages Posted: 20 Jan 2015 Last revised: 13 Nov 2015

See all articles by Hao Xing

Hao Xing

Boston University - Questrom School of Business

Date Written: February 22, 2015

Abstract

In a market with stochastic investment opportunities, we study an optimal consumption investment problem for an agent with recursive utility of Epstein-Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The supperdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein-Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein-Zin aggregator is neither Lipschitz nor jointly concave in all its variables.

Keywords: Portfolio optimization, Epstein-Zin utility, Backward stochastic differential equation

JEL Classification: G11, D91

Suggested Citation

Xing, Hao, Consumption Investment Optimization with Epstein-Zin Utility in Incomplete Markets (February 22, 2015). Available at SSRN: https://ssrn.com/abstract=2551793 or http://dx.doi.org/10.2139/ssrn.2551793

Hao Xing (Contact Author)

Boston University - Questrom School of Business ( email )

595 Commonwealth Avenue
Boston, MA MA 02215
United States

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