Probabilistic Representation and Approximation for Coupled Systems of Variational Inequalities

Details Probabilistic Representation and Approximation for Coupled Systems of Variational Inequalities Probabilistic Representation and Approximation for Coupled Systems of Variational Inequalities

2009-09-05

arxiv.org/abs/0909.0998v2

Statistics and Probability Letters 80, 17-18 (2010) 1388-1396

Mathematics

Probability

Scientific paper

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.

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