Brownian particles controlled by their occupation measure
Résumé
In this article, we study a finite horizon linear-quadratic stochastic control problem for Brownian particles, where the cost functions depend on the state and the occupation measure of the particles. To address this problem, we develop an Itô formula for the flow of occupation measure, which enables us to derive the associated Hamilton-Jacobi-Bellman equation. Then, thanks to a Feynman-Kac formula and the Boué-Dupuis formula, we construct an optimal strategy and an optimal trajectory. Finally, we illustrate our result when the cost-function is the volume of the sausage associated to the particles.
Mots clés
Stochastic optimal control
Occupation measure
Brownian particles
Calculus on the space of measures
Hamilton-Jacobi-Bellman equations
Boué-Dupuis formula
Stochastic optimal control Occupation measure Brownian particles Calculus on the space of measures Hamilton-Jacobi-Bellman equations Boué-Dupuis formula AMS classification: 93E20 49J55 60G57 49L12
Stochastic optimal control
Boué-Dupuis formula AMS classification: 93E20
49J55
60G57
49L12
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)