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Pré-Publication, Document De Travail Année : 2024

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.
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Dates et versions

hal-04540872 , version 1 (10-04-2024)

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Paternité - Pas d'utilisation commerciale

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  • HAL Id : hal-04540872 , version 1

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Loïc Béthencourt, Rémi Catellier, Etienne Tanré. Brownian particles controlled by their occupation measure. 2024. ⟨hal-04540872⟩
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