{"ID":5937683,"CreatedAt":"2026-07-07T03:14:33.014478982Z","UpdatedAt":"2026-07-08T12:38:41.542637154Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.04278","arxiv_id":"2607.04278","title":"Deep Learning for Dynamic Programming with Recursive Utility","abstract":"We propose the first deep learning algorithm, the Certainty Equivalent Learning (CEL) algorithm, for solving high-dimensional discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is numerically challenging because the recursive utility does not have an explicit representation and the Bellman equation contains a certainty equivalent that is difficult to evaluate. The CEL algorithm learns this certainty-equivalent value directly with neural networks and jointly approximates value functions, policy functions, and certainty-equivalent functions. The CEL algorithm is mesh-free and simulation-based, allowing high-dimensional state and control spaces, and does not rely on Euler equations, first-order conditions, or differentiability of the state transition function. The CEL algorithm also works for dynamic programming problems with expected utility as expected utility is a special case of recursive utility. We apply the CEL to discounted linear exponential quadratic Gaussian control, small-noise robust control, Epstein-Zin DSGE, and multivariate strategic asset allocation problems. Compared with closed-form and VFI-based benchmarks, the CEL delivers accurate value and policy approximations, remains effective in high-dimensional problems, achieves accuracy comparable to VFI in the small-noise robust-control case, and produces out-of-sample Bellman errors and Euler or first-order residuals that are in the range from 1.0e-4 to 1.0e-3 for most problems.","short_abstract":"We propose the first deep learning algorithm, the Certainty Equivalent Learning (CEL) algorithm, for solving high-dimensional discrete-time dynamic programming problems with recursive utility. Dynamic programming with recursive utility is numerically challenging because the recursive utility does not have an explicit r...","url_abs":"https://arxiv.org/abs/2607.04278","url_pdf":"https://arxiv.org/pdf/2607.04278v1","authors":"[\"Xianhua Peng\",\"Wu Guo\"]","published":"2026-07-05T12:43:03Z","proceeding":"q-fin.CP","tasks":"[\"q-fin.CP\",\"cs.LG\",\"econ.EM\",\"math.OC\",\"stat.ML\"]","methods":"[\"Large Language Model\"]","has_code":false}