Reflected BSDE associated to jump Markov processes and application to PDE

EDSR Réfléchie associée à un processus markovien de saut et application aux EDP

Khaled Bahlali (1) , Abdelkarim Oualaid (2) , Youssef Ouknine (2)

1 IMATH - Institut de Mathématiques de Toulon - EA 2134
2 LIBMA - Laboratoire Ibn Al-Banna de Mathématiques et Applications

In this paper we study a class of reflected backward stochastic differential equations (RBSDE) driven by the compensated random measure associated to a given pure jump Markov process X on a general state space U. The "reflection" keeps the solution above a given càdlàg process. We prove the uniqueness and existence both by a combination of the Snell envelope theory and fixed point argument. We apply these results to represent probabilitically the value function of some quasi-variational inequalities associated to the Markov process X.

Mots clés: Backward stochastic differential equations; Jump Markov processes; Marked point processes; Quasi-variational inequalities

Domaines: Probabilités [math.PR]

Khaled Bahlali, Abdelkarim Oualaid, Youssef Ouknine. Reflected BSDE associated to jump Markov processes and application to PDE. 2020. ⟨hal-03520315⟩