  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.
