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arXiv · 2502.15138

Optimal Comfortable Consumption under Epstein-Zin utility

Dejian Tian·Weidong Tian·Jianjun Zhou·Zimu Zhu
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Abstract

We solve the optimal portfolio choice problem under Epstein--Zin utility with a time-varying consumption constraint, where closed-form expressions for neither the primal nor the dual value function are available. We establish the dynamic programming principle for the value function and prove that it is a viscosity solution of the corresponding Hamilton--Jacobi--Bellman equation. We further establish the $C^2$ regularity of the value function and derive a verification theorem using stochastic perturbation techniques. Finally, we provide an explicit characterization of the constrained region. The proposed methodology extends naturally to other constrained portfolio choice problems under the Epstein--Zin utility.

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Dejian Tian, Weidong Tian, Jianjun Zhou, Zimu Zhu. 2025-02-21. Optimal Comfortable Consumption under Epstein-Zin utility. https://arxiv.org/abs/2502.15138

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