Abstract: Path-dependent PDEs are PDEs defined on path spaces consisting of continuous or cadlag functions. Those PDEs appear naturally in non-Markovian problems in optimal control, probability, and mathematical finance, for example, optimal control of delay equations or pricing of path-dependent options. In this talk, I will give an overview of the theory of viscosity solutions of path-dependent PDEs of first and second order and I will address recent developments as well as some open problems.
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