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Consumption investment optimization with Epstein-Zin utility in incomplete markets

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  • Hao Xing

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.

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  • Hao Xing, 2015. "Consumption investment optimization with Epstein-Zin utility in incomplete markets," Papers 1501.04747, arXiv.org, revised Nov 2015.
    • Handle: RePEc:arx:papers:1501.04747
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    References listed on IDEAS

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    Cited by:

    1. Anis Matoussi & Hao Xing, 2016. "Convex duality for stochastic differential utility," Papers 1601.03562, arXiv.org.

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