Course No.:21627Z
Period:10
Credits:0.5
Course Category:Lecture
Primary Coverage:
In this mini-course I will present the basic theory of backward di¤erential equations, …rstly introduced by Pardoux and Peng, developed further in recent years by various authors including many talented Chinese scholars such as Y.Hu, J. Ma, J. Yong, X. Y. Zhou etc. My lectures will be based on an functional equation approach, developed recently by Lyons, Liang and myself, which allows us to extend BSDE on a general …ltered probability space. I will cover the following material:
1. Hunt processes, their …ltrations and martingale representation.
2. Non-linear systems of parabolic equations and BSDE, functional equa-
tions, existence and uniqueness.
3. Non-linear Cameron-Martin formula.
4. Non-linear stochastic ‡ows associated with quasi-linear parabolic equa-tions and gradient estimates.
References:
1) N. El Karoui, S. Peng and M. C. Quenez: Backward stochastic differential equation in Finance, Math Finance Vol 7, No. 1 (1997), 1-71.
2) Liang, Lyons and Qian: Backward stochastic dynamics on a …ltered prob-
ability space, arXiv:0904.0377v3.
3) Z. Qian And J. Ying: Martingale representations for di¤usion processes.
arXiv:0910.4911v1.
4) Liang and Qian: Girsanov’s theorem for BSDE and non-linear ‡ows for
quasi-linear parabolic system. Preprint.
Author:Zhongmin Qian