| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 25 | |
| Number of page(s) | 28 | |
| DOI | https://doi.org/10.1051/cocv/2023015 | |
| Published online | 30 March 2023 | |
Probabilistic representation of viscosity solutions to quasi-variational inequalities with non-local drivers*
Department of Physics and Electrical Engineering, Linnaeus University,
Växjö, Sweden
* Corresponding author: perninge@kth.se
Received:
9
October
2022
Accepted:
6
March
2023
We consider quasi-variational inequalities (QVIs) with general non-local drivers and related systems of reflected backward stochastic differential equations (BSDEs) in a Brownian filtration. We show existence and uniqueness of viscosity solutions to the QVIs by first considering the standard (local) setting and then applying a contraction argument. In addition, the contraction argument yields existence and uniqueness of solutions to the related systems of reflected BSDEs and extends the theory of probabilistic representations of PDEs in terms of BSDEs to our specific setting.
Mathematics Subject Classification: 60G40 / 93E20 / 49L20
Key words: Backward stochastic differential equations / impulse control / partial differential equations / viscosity solutions / quasi-variational inequalities
© The authors. Published by EDP Sciences, SMAI 2023
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