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Erschienen in:
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2017 | OriginalPaper | Buchkapitel

11. Path Dependent PDEs

verfasst von : Jianfeng Zhang

Erschienen in: Backward Stochastic Differential Equations

Verlag: Springer New York

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Abstract

The path dependent PDEs (PPDE, for short) is a powerful and convenient tool for non-Markov problems. In particular, a BSDE can be viewed as a semilinear PPDE and thus the nonlinear Feynman-Kac formula is extended to non-Markov case. In this chapter we are most interested in fully nonlinear parabolic PPDEs, typically path dependent Hamilton-Jacobi-Bellman equations and path dependent Bellman-Isaacs equations, due to their important applications in stochastic control and stochastic differential games. However, in path dependent case, even a heat equation may not have a classical solution. We thus turn to viscosity solutions. We shall introduce a new notion of viscosity solution and establish its well-posedness, including the comparison principle.

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Vorheriges Kapitel Nonlinear Expectation
Nächstes Kapitel Second Order BSDEs
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Metadaten
Titel
Path Dependent PDEs
verfasst von
Jianfeng Zhang
Copyright-Jahr
2017
Verlag
Springer New York
Buch
Backward Stochastic Differential Equations

Print ISBN: 978-1-4939-7254-8

Electronic ISBN: 978-1-4939-7256-2

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-1-4939-7256-2_11