Viscosity solutions of obstacle problems for fully nonlinear path-dependent PDEs

Ibrahim Ekren

Stochastic Processes and their Applications, 2017, vol. 127, issue 12, 3966-3996

Abstract: In this article, we adapt the definition of viscosity solutions to the obstacle problem for fully nonlinear path-dependent PDEs with data uniformly continuous in (t,ω), and generator Lipschitz continuous in (y,z,γ). We prove that our definition of viscosity solutions is consistent with the classical solutions, and satisfy a stability result. We show that the value functional defined via the second order reflected backward stochastic differential equation is the unique viscosity solution of the variational inequalities.

Keywords: Path-dependent PDEs; Viscosity solutions; Reflected backward stochastic differential equations; Variational inequalities (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:12:p:3966-3996

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DOI: 10.1016/j.spa.2017.03.016

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