Viscosity Solutions of Path Dependent PDEs

When
Start: 04/11/2016 - 4:15pm
End  : 04/11/2016 - 5:15pm

Category
Applied Math Seminar

Speaker
Jianfeng Zhang (USC)

Abstract

Abstract: Path dependent PDEs considers continuous paths as its variable. It is a convenient tool for stochastic optimization/games in non-Markovian setting, and has natural applications on non-Markovian financial models with drift and/or volatility uncertainty. For example, a martingale can be viewed as a solution to a path dependent heat equation, and we are particularly interested in path dependent HJB equations and Isaacs equations. In path dependent case, even a heat equation typically does not have a classical solution, where smoothness is defined through Dupire's functional Ito calculus, so a viscosity theory is desirable. There are two major difficulties in the project: (i) the state space of (continuous paths) is not locally compact, and thus one cannot apply many tools in standard viscosity theory; (ii) fully nonlinear PPDEs involve a nonlinear expectation under which the dominated convergence theorem fails. In this talk, we will motivate our definition of viscosity solutions and give an overview of the recent developments of the theory.

Where
Emmy Noether Room Millikan 1021 Pomona College