Probabilistic Representation and Approximation for Coupled Systems of Variational Inequalities

Romuald Elie (1, 2) , Idris Kharroubi (1, 2)

1 CREST - Centre de Recherche en Économie et Statistique
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Our study is dedicated to the probabilistic representation and numerical approximation of solutions to coupled systems of variational inequalities. The dynamics of each component of the solution is driven by a different linear parabolic operator and suffers a non-linear dependence in all the components of the solution. This dynamics is combined with a global structural constraint between all the components of the solution including the practical example of optimal switching problems. In this paper, we interpret the unique viscosity solution to this type of coupled systems of variational inequalities as the solution to one-dimensional constrained BSDEs with jumps introduced recently in [6]. In the spirit of [3], this new representation allows for the introduction of a natural entirely probabilistic numerical scheme for the resolution of these systems.

Mots clés: BSDE with jumps; variational inequalities; viscosity solutions; Monte Carlo simulations; Switching problems

Domaines: Probabilités [math.PR]

Romuald Elie, Idris Kharroubi. Probabilistic Representation and Approximation for Coupled Systems of Variational Inequalities. Statistics and Probability Letters, 2010, 80 (17-18), pp.1388-1396. ⟨hal-00413161v2⟩