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

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  • Ekren, Ibrahim

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.

Suggested Citation

  • Ekren, Ibrahim, 2017. "Viscosity solutions of obstacle problems for fully nonlinear path-dependent PDEs," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3966-3996.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:12:p:3966-3996
    DOI: 10.1016/j.spa.2017.03.016
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    References listed on IDEAS

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    1. Hamadène, S. & Lepeltier, J. -P., 2000. "Reflected BSDEs and mixed game problem," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 177-188, February.
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