Reflected generalized BDSDEs driven by non-homogeneous Lévy processes and obstacle problems for stochastic integro-PDEs with nonlinear Neumann boundary conditions

2025/09/30 by Elmansouri, Badr, Elhachemy, Mohammed, Marzougue, Mohamed +1
#60H05 #60H15 #60H20 #60H30 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.25912

Abstract

We consider reflected generalized backward doubly stochastic differential equations driven by a non-homogeneous Lévy process. Under stochastic conditions on the coefficients, we prove the existence and uniqueness of a solution. Furthermore, we apply these results to obtain a probabilistic representation for the viscosity solutions of an obstacle problem governed by stochastic integro-partial differential equations with a nonlinear Neumann boundary condition.

Citations

• Optimal reinsurance via BSDEs in a partially observable model with jump clusters
• Reflected generalized backward doubly SDEs driven by Lévy processes and Applications
• Conjugate convex functions in optimal stochastic control

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