{"ID":2895743,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.08657","arxiv_id":"2507.08657","title":"Causal Hamilton-Jacobi-Bellman Equations for Anticipative Stochastic Optimal Control","abstract":"We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential equation. We combine the martingale optimality principle with a functional form of Itô's formula to derive a Hamilton-Jacobi-Bellman (HJB) equation for this problem. This HJB equation is formulated in terms of Dupire's functional derivatives and involves a transport equation arising from the anticipativity of the problem.","short_abstract":"We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential equation. We combine the martingale optimality principle with a functional form of Itô'...","url_abs":"https://arxiv.org/abs/2507.08657","url_pdf":"https://arxiv.org/pdf/2507.08657v2","authors":"[\"Peter Bank\",\"Franziska Bielert\"]","published":"2025-07-11T15:00:05Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Large Language Model\"]","has_code":false}