Viscosity Solutions of Systems of Variational Inequalities with Interconnected Bilateral Obstacles

Boualem Djehiche (1) , Said Hamadène (2) , Marie Amélie Morlais (2)

1 KTH - Department of Mathematics [Sweden]
2 LMM - Laboratoire Manceau de Mathématiques

We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward SDEs, we construct a continuous viscosity solution of polynomial growth. Moreover, we establish a comparison result which in turn yields uniqueness of the solution.

Mots clés: AMS Classification subjects: 49N70; Switching games; variational inequalities; oblique reflection; penalization; backward stochastic dif-; ferential equation; Bellman-Isaacs equation; Perron's method

Domaines: Probabilités [math.PR]; Optimisation et contrôle [math.OC]

Boualem Djehiche, Said Hamadène, Marie Amélie Morlais. Viscosity Solutions of Systems of Variational Inequalities with Interconnected Bilateral Obstacles. 2018. ⟨hal-01835105⟩