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

Battle Count: 118

The paper provides rigorous theoretical foundations for portfolio optimization under Epstein-Zin preferences with leverage constraints, which are highly relevant to quantitative trading. Epstein-Zin preferences are widely used in asset pricing (long-run risk literature) and the leverage constraint is economically important for margin requirements and borrowing limits. However, the paper is purely theoretical with no numerical implementations, backtests, or trading strategies. The explicit solutions for proportional and constant leverage cases could inform practical portfolio construction. The feedback-form optimal strategies (Theorem 3.2) provide actionable structure for quantitative portfolio managers.

The paper is extremely complex from a mathematical standpoint, involving: (1) non-Lipschitz Epstein-Zin aggregators requiring novel BSDE techniques, (2) viscosity solution theory for HJB equations with state-dependent constraints, (3) dynamic programming principles for time-inhomogeneous infinite-horizon problems, (4) comparison principles for elliptic differential operators, (5) smooth-fit conditions at free boundaries, and (6) highly nonlinear ODEs in constrained/unconstrained regions. Implementing the theoretical results numerically would require solving coupled nonlinear ODEs with free boundaries, which is non-trivial. The explicit solutions (Proposition 7.1) are straightforward to implement, but the general case requires sophisticated numerical PDE methods.

As a purely theoretical paper with complete mathematical proofs (Theorems 3.1, 3.2, 3.3 and supporting lemmas/propositions), reproducibility is assessed by the ability to verify the proofs. All assumptions are clearly stated (Black-Scholes market, Epstein-Zin aggregator with nu in (0,1), 0<R<1, Lipschitz concave leverage function g). The proofs are self-contained with technical details in Appendices A-D. No computational experiments are needed to verify the results.