| Summary: | We investigate the stability of the Epstein-Zin problem with
respect to small distortions in the dynamics of the traded securities. We
work in incomplete market model settings, where our parametrization
of perturbations allows for joint distortions in returns and volatility of
the risky assets and the interest rate. Considering empirically the most
relevant specifications of risk aversion and elasticity of intertemporal
substitution, we provide a condition that guarantees the convexity of
the domain of the underlying problem and results in the existence and
uniqueness of a solution to it. Then, we prove the convergence of the
optimal consumption streams, the associated wealth processes, the indirect utility processes, and the value functions in the limit when the
model perturbations vanish.
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