Survey on Path-Dependent PDEs

Abstract

In this paper, the authors provide a brief introduction of the path-dependent partial di.erential equations (PDEs for short) in the space of continuous paths, where the path derivatives are in the Dupire (rather than Fréchet) sense. They present the connections between Wiener expectation, backward stochastic di.erential equations (BSDEs for short) and path-dependent PDEs. They also consider the well-posedness of path-dependent PDEs, including classical solutions, Sobolev solutions and viscosity solutions.

Keywords

Path-Dependent / Wiener expectation / BSDEs / Classical solution / Sobolev solution / Viscosity solution

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