Viscosity solutions of systems of PDEs with interconnected obstacles and switching problem without monotonicity condition

Article type: Research Article

Authors: Hamadène, Said^a | Mnif, Mohamed^{b; *} | Neffati, Sarra^{b; a}

Affiliations: [a] LMM, Le Mans Université, Avenue Olivier Messiaen, 72085 Le Mans, Cedex 9, France. E-mail: hamadene@univ-lemans.fr | [b] University of Tunis El Manar, ENIT-LAMSIN, B.P. 37, 1002 Tunis Belvédère, Tunisia. E-mails: mohamed.mnif@enit.rnu.tn, sarra.neffati@enit.utm.tn

Correspondence: [*] Corresponding author. E-mail: mohamed.mnif@enit.rnu.tn.

Abstract: We show the existence and uniqueness of a continuous viscosity solution of a system of partial differential equations (PDEs for short) without assuming the usual monotonicity conditions on the driver function as in Hamadène and Morlais’s article [Applied Mathematics & Optimization 67 (2013), 163–196]. Our method strongly relies on the link between PDEs and reflected backward stochastic differential equations with interconnected obstacles for which we already know that the solution exists and is unique for general drivers.

Keywords: Partial differential equations, interconnected obstacles, viscosity solution, multi-modes switching, HJB system, reflected backward stochastic differential equations

DOI: 10.3233/ASY-181508

Journal: Asymptotic Analysis, vol. 113, no. 3, pp. 123-136, 2019