Non-Markovian Fully Coupled Forward-Backward Stochastic Systems and Classical Solutions of Path-dependent PDEs

Details Non-Markovian Fully Coupled Forward-Backward Stochastic Systems and Classical Solutions of Path-dependent PDEs Non-Markovian Fully Coupled Forward-Backward Stochastic Systems and Classical Solutions of Path-dependent PDEs

2012-04-16

arxiv.org/abs/1204.3351v1

Mathematics

Probability

arXiv admin note: text overlap with arXiv:1108.4317

Scientific paper

This paper explores the relationship between non-Markovian fully coupled forward-backward stochastic systems and path-dependent PDEs. The definition of classical solution for the path-dependent PDE is given within the framework of functional It\^{o} calculus. Under mild hypotheses, we prove that the forward-backward stochastic system provides the unique classical solution to the path-dependent PDE.

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