| □2010.11.26 16:30-18:00 開催 |
| Numerical Algorithms for Backward Stochastic Differential Equations: Convergence and Simulations (後向き確率微分方程式の数値アルゴリズム：収束とシミュレーション ) |
| 講演者：Dr. Mingyu Xu, Institute of Applied Mathematics, Academy of Mathematics
and Systems Science, Chinese Academy of Sciences (CN) |
Abstract:
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 $(t,\omega )$.
For many nonlinear cases of $g$, we can not find the solution explicitly. Here we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and give simulation results for different types of BSDEs. At last, some recent approaches on multi-dimensional case is also presented.
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