Viscosity Solutions of Path-dependent Integro-differential Equations
Analysis of PDEs
2014-12-31 v1 Probability
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.
Cite
@article{arxiv.1412.8495,
title = {Viscosity Solutions of Path-dependent Integro-differential Equations},
author = {Christian Keller},
journal= {arXiv preprint arXiv:1412.8495},
year = {2014}
}