Multivalued backward stochastic differential equations with jumps and moving boundary

Résumé

We establish existence and uniqueness results for a one-dimensional multivalued backward stochastic differential equation (MBSDE) with jumps. The equation involves a time-indexed family of maximal monotone operators kt(⋅) associated with increasing functions k(t,⋅) taking values in R− and defined on intervals with time-dependent boundaries. The existence result is obtained via a penalization method, under standard Lipschitz conditions on the driver with respect to (y,z), a monotonicity condition in the jump component ψ, square-integrability assumptions on the terminal condition and the driver, and suitable local-in-time integrability conditions on k(⋅,y). We further extend these results to the general case where the operators kt(⋅) take values in R and act on unbounded domains.

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