Date/heure
27 mars 2025
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Manal Jakani (ENSAE)
Catégorie d'évènement
Séminaire Probabilités et Statistique
Résumé
We study a system of partial differential equations (PDEs) with interconnected obstacles and Neumann-type boundary conditions on a smooth bounded domain D. This system is the Hamilton-Jacobi-Bellman system of equations associated with multidimensional switching problem in finite horizon when the state process is constrained to live in the domain D. We prove the existence of a unique continuous viscosity solution. The existence of a viscosity solution is obtained using a probabilistic approach which connects the system of PDEs to a system of backward stochastic differential equations, where randomness is constrained to stay in the domain D. The second main result consists in verifying the maximum principle, which ensures the comparison between any viscosity sub-solution and super-solution of the PDEs system. This guarantees the uniqueness and continuity of the solution.