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Viscosity solutions of path-dependent integro-differential equations

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  • Keller, Christian

Abstract

We extend the notion of viscosity solutions for path-dependent PDEs introduced by Ekren et al. (2014) to path-dependent integro-differential equations and establish well-posedness, i.e., existence, uniqueness, and stability, for a class of semilinear path-dependent integro-differential equations with uniformly continuous data. Closely related are non-Markovian backward SDEs with jumps, which provide a probabilistic representation for solutions of our equations. The results are potentially useful for applications using non-Markovian jump–diffusion models.

Suggested Citation

  • Keller, Christian, 2016. "Viscosity solutions of path-dependent integro-differential equations," Stochastic Processes and their Applications, Elsevier, vol. 126(9), pages 2665-2718.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:9:p:2665-2718
    DOI: 10.1016/j.spa.2016.02.014
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    References listed on IDEAS

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    1. Bayraktar, Erhan & Yao, Song, 2012. "Quadratic reflected BSDEs with unbounded obstacles," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1155-1203.
    2. Neufeld, Ariel & Nutz, Marcel, 2014. "Measurability of semimartingale characteristics with respect to the probability law," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3819-3845.
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