Optimal Consumption-Investment with Epstein-Zin Utility under Leverage Constraint

Fuente: arXiv
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Main Authors: Tian, Dejian, Tian, Weidong, Zhou, Jianjun, Zhu, Zimu
Format: Preprint
Published: 2025
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author Tian, Dejian
Tian, Weidong
Zhou, Jianjun
Zhu, Zimu
author_facet Tian, Dejian
Tian, Weidong
Zhou, Jianjun
Zhu, Zimu
contents We study optimal portfolio choice under Epstein-Zin recursive utility in the presence of general leverage constraints. We first establish that the optimal value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, by developing a new dynamic programming principle under constraints. We further demonstrate that the value function admits smoothness and characterize the optimal consumption and investment strategies. In addition, we derive explicit solutions for the optimal strategy and explicitly delineate the constrained and unconstrained regions in several special cases of the leverage constraint. Finally, we conduct a comparative analysis, highlighting the differences relative to the classical time-separable preferences and to the setting without leverage constraints.
format Preprint
id arxiv_https___arxiv_org_abs_2509_21929
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Optimal Consumption-Investment with Epstein-Zin Utility under Leverage Constraint
Tian, Dejian
Tian, Weidong
Zhou, Jianjun
Zhu, Zimu
Portfolio Management
49L20, 60H20, 91G10, 91G80, 93E20
We study optimal portfolio choice under Epstein-Zin recursive utility in the presence of general leverage constraints. We first establish that the optimal value function is the unique viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation, by developing a new dynamic programming principle under constraints. We further demonstrate that the value function admits smoothness and characterize the optimal consumption and investment strategies. In addition, we derive explicit solutions for the optimal strategy and explicitly delineate the constrained and unconstrained regions in several special cases of the leverage constraint. Finally, we conduct a comparative analysis, highlighting the differences relative to the classical time-separable preferences and to the setting without leverage constraints.
title Optimal Consumption-Investment with Epstein-Zin Utility under Leverage Constraint
topic Portfolio Management
49L20, 60H20, 91G10, 91G80, 93E20
url https://arxiv.org/abs/2509.21929