Infinite Horizon Optimal Consumption: Intertemporal Hedging under Epstein-Zin Preferences

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The paper provides a rigorous theoretical framework for optimal consumption-investment under Epstein-Zin preferences in incomplete markets with stochastic investment opportunities. While primarily theoretical, the variational characterization offers a practical numerical scheme for computing optimal policies. The fat-tailed excess return analysis is directly relevant to quantitative trading as it demonstrates how distributional assumptions materially affect optimal consumption and hedging policies. The intertemporal hedging component is relevant for multi-asset portfolio management. However, the paper does not address high-frequency trading, execution, or direct alpha generation.

Implementation requires solving a non-convex variational problem (minimizing functional I(g) over a weighted Sobolev space), which involves discretizing the functional and solving the associated Euler-Lagrange equation (a second-order semilinear ODE). The verification theorem requires constructing the myopic probability measure, solving Epstein-Zin BSDEs, and applying perturbation arguments. The numerical scheme from Guasoni et al. [17] must be adapted for the non-convex case. Requires strong background in functional analysis, PDE theory, and stochastic calculus.

The paper is primarily theoretical with complete proofs provided in the appendix. Numerical examples (CIR state variable, Kim-Omberg, fat-tailed excess returns) include specific parameter values and reference the numerical scheme from Guasoni et al. [17]. However, no code or computational scripts are provided. The theoretical framework is fully self-contained with all assumptions stated explicitly.