ESAIM Control Optimisation and Calculus of Variations· 2026Q1
Dynamic Programming Principle for Stochastic Control Problems on Riemannian Manifolds
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- 2026year
Short summary
A dynamic programming principle and Hamilton-Jacobi-Bellman (HJB) equation are established for stochastic optimal control problems on compact Riemannian manifolds without boundary.
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Key points
- Establishes the dynamic programming principle for stochastic optimal control on compact Riemannian manifolds.
- Derives the associated Hamilton-Jacobi-Bellman (HJB) equation for the value function.
- Proves existence, uniqueness, and continuous dependence of viscosity solutions to the HJB equation.
- Presents a verification theorem to characterize optimal controls.
AI-generated from the title and abstract; the full text is not read.
Abstract
In this paper, we first establish the dynamic programming principle for stochastic optimal control problems defined on compact Riemannian manifolds without boundary. Subsequently, we derive the associated Hamilton-Jacobi-Bellman (HJB) equation for the value function. We then prove the existence, uniqueness of viscosity solutions to the HJB equation, along with their continuous dependence on initial data and model parameters. Finally, under appropriate regularity conditions on the value function, we establish a verification theorem that characterizes optimal controls.
The authors' abstract, as published at the source. ESAIM Control Optimisation and Calculus of Variations, 2026 · DOI ↗
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Field: Finance
FinanceEconomics, Econometrics and Finance