Viscosity Solutions of Systems of Variational Inequalities with   Interconnected Bilateral Obstacles
  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. 
Boualem Djehiche, Said Hamadene and Marie Amelie Morlais
math.AP