Stability of the Epstein–Zin problem
研究了当交易证券的收益率和波动率存在微小扰动时，Epstein-Zin问题是否稳定，给出了保证解存在且唯一的条件，并证明了最优消费、财富和效用函数在扰动消失时收敛。
Abstract 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.