Date: Monday, April 09, 2012
Location: 1360 East Hall (3:00 PM to 4:00 PM)
Title: Viscosity Solutions of Path Dependent PDEs
Abstract: It is well known that Markovian BSDEs (resp. 2BSDEs) provides a probabilistic representation for the viscosity solution of a semi-linear (resp. fully nonlinear) parabolic PDE. In this talk we shall introduce a type of parabolic Path Dependent PDEs (PPDEs, for short) and propose a notion of its viscosity solutions, and thus extends the above results to non-Markovian (or path dependent) cases. As in the viscosity theory of standard PDEs, we shall prove the existence, uniqueness, and stability of viscosity solutions. The crucial step for uniqueness is to prove the comparison principle. In standard theory, the arguments rely heavily on the compactness of the state space, which is not true in the path dependent case. We decompose the problem into a partial comparison principle and a variation of the Peron's method.
Speaker: Jianfeng Zhang
Institution: USC
Event Organizer: Erhan Bayraktar erhan@umich.edu
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