Probabilistic Representation of Viscosity Solutions to Quasi-Variational Inequalities with Non-Local Drivers

2022/10/05 by Magnus Perninge, Perninge, Magnus
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2210.02417

Abstract

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.

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