PreprintCC BY 4.0HAL
Viscosity solution of systems of integral-partial differential equations with interconnected obstacles without Monotonicity Conditions and infinite Lévy measure
Abstract
In this paper, we study a system of second-order integral-partial differential equations with interconnected obstacles. A particular case, is the Hamilton-Jacobi-Bellman (HJB for short) system associated with the optimal switching problem in the jump-diffusion model. Getting rid of the monotonicity condition on the generators with respect to the jump component, we construct a continuous viscosity solution of the system, which is unique in the class of continuous bounded functions. The Lévy measure λ(.) is of infinite activity. The main tool we use is the associated system of reflected backward stochastic differential equations with jumps and interconnected obstacles for which we also study existence and uniqueness of the solution.
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BibTeX
@misc{hamadene2026viscosity,
title = {{Viscosity solution of systems of integral-partial differential equations with interconnected obstacles without Monotonicity Conditions and infinite Lévy measure}},
author = {Said Hamadène and Mohamed Mnif and Sarra Neffati},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16812},
eprint = {2609.16812},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05734756v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Viscosity solution of systems of integral-partial differential equations with interconnected obstacles without Monotonicity Conditions and infinite Lévy measure
AU - Said Hamadène
AU - Mohamed Mnif
AU - Sarra Neffati
PY - 2026
DA - 2026/09/01
PB - HAL
DO - 10.48550/arxiv.2609.16812
UR - https://hal.science/hal-05734756v1
AB - In this paper, we study a system of second-order integral-partial differential equations with interconnected obstacles. A particular case, is the Hamilton-Jacobi-Bellman (HJB for short) system associated with the optimal switching problem in the jump-diffusion model. Getting rid of the monotonicity condition on the generators with respect to the jump component, we construct a continuous viscosity solution of the system, which is unique in the class of continuous bounded functions. The Lévy measure λ(.) is of infinite activity. The main tool we use is the associated system of reflected backward stochastic differential equations with jumps and interconnected obstacles for which we also study existence and uniqueness of the solution.
ER -