Work

Brownian Particles Controlled by Their Occupation Measure

Year: 2025

Type: article

Abstract: . 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 HJB equation. Then, thanks to a Feynman–Kac formula and the Boué–Dupuis formula [Boué and Dupuis, Ann. Probab., 26 (1998), pp. 1641–1659], 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.

Source: SIAM Journal on Control and Optimization

DOI: 10.1137/24m1656220

Authors: Loïc Béthencourt, Rémi Catellier, Etienne Tanré

Institutions: Centre National de la Recherche Scientifique, Université Côte d'Azur, Laboratoire Jean-Alexandre Dieudonné, Institut national de recherche en sciences et technologies du numérique

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Analysis Modelling Simulation Multiscale