Mingyu Xu Institute of Applied Mathematics, Chinese Academy of Sciences
Title: Stochastic simulation: from Brownian motion to BSDE
Non-linear backward stochastic differential equations (BSDEs in short) were firstly introduced by Pardoux and Peng (\cite{PP1990}, 1990), who proved the existence and uniqueness of the adapted solution, under smooth square integrability assumptions on the coefficient and the terminal condition, and when the coefficient $g(t,\omega ,y,z)$ is Lipschitz in $(y,z)$ uniformly in $(t,\omega )$. From then on, the theory of backward stochastic differential equations (BSDE) has been widely and rapidly developed. And many problems in mathematical finance can be treated as BSDEs. The natural connection between BSDE and partial differential equations (PDE) of parabolic and elliptic types is also important applications. In this talk, we study numerical algorithm and simulation of BSDE. We begin from some basic stochastic simulation, then consider simulations for BSDE, and prove the convegence result.
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Last Modified: February 26, 2009