Systems of reflected BSDEs with interconnected bilateral obstalces: Existence, Uniqueness and Applications

Said Hamadène (1) , Tingshu Mu (2)

1 LMM - Laboratoire Manceau de Mathématiques
2 LMM - Laboratoire de modélisation en mécanique

This paper is related to the study of systems of reflected backward stochastic differential equations with interconnected bilateral obstacles. These systems are connected with zero-sum stochastic switching games. Under appropriate assumptions, we provide either existence or existence and uniqueness of the solution of those systems when the switching costs are Itô processes. The link with systems of PDEs with bilateral interconnected obstacles is also stated via the Feynman-Kac representation when randomness comes from a Markov diffusion process. AMS Classification subjects: 93C30 ; 91A15 ; 93E20 ; 49J20.

Mots clés: Systems of reflected BSDEs; Bilateral interconnected obstacles; Zero-sum stochastic switching games; Optimal switching; Systems of PDEs with interconnected obstacles; Feynman-Kac representation; Viscosity solution

Domaines: Probabilités [math.PR]

Said Hamadène, Tingshu Mu. Systems of reflected BSDEs with interconnected bilateral obstalces: Existence, Uniqueness and Applications. 2019. ⟨hal-01973450⟩