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Probability and Computational Finance Seminar
Ibrahim Ekren University of Southern California Title: Path-dependent heat equation as an introduction to viscosity solutions of PPDEs Abstract: In this talk, we define derivatives of functionals on the space of continuous paths and give an introduction to path-dependent partial differential equations (PPDEs). Since the space of continuous paths is not locally compact, we cannot rely on the theory of viscosity solutions for PDEs and need to develop a new approach. We focus on the path-dependent heat equation and link it to a control problem. We define viscosity solution of the path-dependent heat equation and prove its uniqueness. We will also point out the main difficulties of fully nonliear PPDEs and mention some applications. This talk is based on joint works with Christian Keller, Nizar Touzi and Jianfeng Zhang. Date: Monday, January 13, 2014Time: 5:00 pmLocation: Wean Hall 8220Submitted by: Steve ShreveNote: THE SEMINAR HAS MOVED TO WEAN HALL 8220. |