{"ID":3006121,"CreatedAt":"2026-06-03T03:09:48.883664427Z","UpdatedAt":"2026-06-04T19:14:31.964469513Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.02945","arxiv_id":"2606.02945","title":"Infinite Horizon Optimal Consumption: Intertemporal Hedging under Epstein-Zin Preferences","abstract":"We study an infinite-horizon optimal consumption-investment problem for an investor with Epstein-Zin stochastic differential utility with stochastic investment opportunities in an incomplete market. Risk aversion and intertemporal substitution are separated, and we work in the regime $θ\\in(0,1)$, where there exists a unique generalised utility process for arbitrary non-negative progressively measurable consumption streams. Our main contribution is a variational characterisation of the value function. We show that the value function is the unique minimiser of a functional whose Euler-Lagrange equation coincides with the Hamilton-Jacobi-Bellman equation. Although the functional may be non-convex, the direct method yields existence, and we prove every minimiser is strictly positive, bounded, and classical. A verification theorem identifies any minimiser with the value function and gives feedback representations for optimal consumption and investment policies. The proof combines a change of measure to the myopic probability with uniqueness results for Epstein-Zin BSDEs and a perturbation argument for optimality. Examples with stochastic volatility, Gaussian excess returns, and fat-tailed excess returns illustrate the scope of the framework and its implications for intertemporal hedging.","short_abstract":"We study an infinite-horizon optimal consumption-investment problem for an investor with Epstein-Zin stochastic differential utility with stochastic investment opportunities in an incomplete market. Risk aversion and intertemporal substitution are separated, and we work in the regime $θ\\in(0,1)$, where there exists a u...","url_abs":"https://arxiv.org/abs/2606.02945","url_pdf":"https://arxiv.org/pdf/2606.02945v1","authors":"[\"Erhan Bayraktar\",\"Emmet Lawless\"]","published":"2026-06-01T22:53:18Z","proceeding":"q-fin.MF","tasks":"[\"q-fin.MF\",\"math.OC\",\"q-fin.PM\"]","methods":"[\"Large Language Model\"]","has_code":false}