Viscosity Solutions of Path-dependent Integro-differential Equations

2014/12/29 by Christian Keller, Keller, Christian
Mathematics · #35D40 #45K05 #60H10 #60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR #msc:35D40 #msc:45K05 #msc:60H10 #msc:60H30

paper · pdf · doi:10.48550/arxiv.1412.8495

arxiv created 2014/12/29 · arxiv updated 2014/12/31

Abstract

We extend the notion of viscosity solutions for path-dependent PDEs introduced by Ekren et al. [Ann. Probab. 42 (2014), no. 1, 204-236] 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.

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