A Minimality Property of the Value Function in Optimal Control on Spaces of Probability Measures
Abstract
Abstract. An optimal control problem with (possibly) unbounded terminal cost is considered in [Formula: see text], the space of Borel probability measures with finite second moment. We consider a suitable weak topology rendering [Formula: see text] locally compact. In this setting, we show that the value function of a control problem is the minimal viscosity supersolution of an appropriate Hamilton–Jacobi–Bellman (HJB) equation. Additionally, if the terminal cost is bounded and continuous, we show that the value function is the unique viscosity solution of the HJB equation.
Fields of Study & Subjects
Stochastic processes and financial applications
Aquatic and Environmental Studies
Optimization and Variational Analysis
Publication details
- Journal / source
- SIAM Journal on Control and Optimization
- Volume
- 64
- Issue
- 1
- Pages
- 1–23
- Publication date
- 2 January 2026
- Language
- EN