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Stability of the Epstein–Zin problem

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  • Michael Monoyios
  • Oleksii Mostovyi

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.

Suggested Citation

  • Michael Monoyios & Oleksii Mostovyi, 2024. "Stability of the Epstein–Zin problem," Mathematical Finance, Wiley Blackwell, vol. 34(4), pages 1263-1290, October.
    • Handle: RePEc:bla:mathfi:v:34:y:2024:i:4:p:1263-1290
    DOI: 10.1111/mafi.12434
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