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

ArXiv ID: 2509.21929 “View on arXiv”

Authors: Dejian Tian, Weidong Tian, Jianjun Zhou, Zimu Zhu

Abstract

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.

Keywords: Epstein-Zin recursive utility, Hamilton-Jacobi-Bellman (HJB) equation, Viscosity solution, Leverage constraints, Dynamic programming, Portfolio Management

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats
  • Why: The paper presents a highly theoretical analysis using advanced mathematics like viscosity solutions and BSDEs, with no empirical data, backtests, or implementation details.
  flowchart TD
    A["Research Goal:<br>Optimal Portfolio Choice with<br>Epstein-Zin Utility & Leverage Constraints"] --> B["Key Methodology:<br>Dynamic Programming &<br>Viscosity Solution Theory"]
    B --> C{"Data/Inputs:<br>General Leverage Constraints &<br>Epstein-Zin Recursive Utility"}
    C --> D["Computational Process:<br>Solve HJB Equation<br>Establish Existence & Uniqueness"]
    D --> E["Key Finding 1:<br>Smoothness of Value Function<br>& Characterized Optimal Strategies"]
    D --> F["Key Finding 2:<br>Explicit Solutions Derived<br>& Constrained/Unconstrained Regions Identified"]
    D --> G["Key Finding 3:<br>Comparative Analysis:<br>vs. Time-Separable & Unconstrained Models"]