Work

Multivalued backward stochastic differential equations with jumps and moving boundary

Year: 2026

Type: article

Abstract: 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.

Source: Stochastic Analysis and Applications

DOI: 10.1080/07362994.2026.2706146

Authors: Badr Elmansouri, Anas Ouknine, Youssef Ouknine

Institutions: Cadi Ayyad University, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques Raphaël Salem, Université de Rouen Normandie, Université Mohammed VI Polytechnique

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W4416781463

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