Viscosity Solutions of system of PDEs with Interconnected Obstacles and nonlinear Neumann Boundary Conditions

Brahim Boufoussi (1) , Said Hamadène (2) , Manal Jakani (2, 3)

1 UCA - Université Cadi Ayyad [Marrakech]
2 LMM - Laboratoire Manceau de Mathématiques
3 LIBMA - Laboratoire Ibn Al-Banna de Mathématiques et Applications

This paper investigates the Hamilton-Jacobi-Bellman system of equations associated with the m-states optimal switching problem in finite horizon when the state process lives in a connected bounded closed domain. We show existence and uniqueness of the solution in viscosity sense of the system. We use systems of generalized reflected backward stochastic differential equations with oblique reflection and the Feynman-Kac representation of their solutions in the Markovian framework.

Mots clés: Generalized Reflected Backward stochastic differential equations; Viscosity solution of PDEs; Variational inequalities; Nonlinear Neumann Boundary conditions; Optimal switching

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Brahim Boufoussi, Said Hamadène, Manal Jakani. Viscosity Solutions of system of PDEs with Interconnected Obstacles and nonlinear Neumann Boundary Conditions. 2022. ⟨hal-03120824v2⟩