Abstract
In this paper, we study the optimal consumption and investment problems for an individual with the Epstein-Zin type utility. We employ the binomial tree model for dynamics of the risky asset and derive optimal policies. We show that the optimal policies converge to those in the continuous-time model of Schroder and Skiadas. The convergence rate of optimal policies is of the order of equal to the time interval between consecutive time points, and there is little difference in convergence rates between CRRA and Epstein-Zin utilities. We also show that the optimal consumption decreases as the elasticity of intertemporal substitution increases.
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