NDLI: Four step scheme for general Markovian forward-backward SDES

Content Provider	Springer Nature Link
Author	Ma, Jin Yong, Jiongmin Zhao, Yanhong
Copyright Year	2010
Abstract	This paper studies a class of forward-backward stochastic differential equations (FBSDE) in a general Markovian framework. The forward SDE represents a large class of strong Markov semimartingales, and the backward generator requires only mild regularity assumptions. The authors show that the Four Step Scheme introduced by Ma, et al. (1994) is still effective in this case. Namely, the authors show that the adapted solution of the FBSDE exists and is unique over any prescribed time duration; and the backward components can be determined explicitly by the forward component via the classical solution to a system of parabolic integro-partial differential equations. An important consequence the authors would like to draw from this fact is that, contrary to the general belief, in a Markovian set-up the martingale representation theorem is no longer the reason for the well-posedness of the FBSDE, but rather a consequence of the existence of the solution of the decoupling integralpartial differential equation. Finally, the authors briefly discuss the possibility of reducing the regularity requirements of the coefficients by using a scheme proposed by F. Delarue (2002) to the current case.
Starting Page	546
Ending Page	571
Page Count	26
File Format	PDF
ISSN	10096124
Journal	Journal of Systems Science and Complexity
Volume Number	23
Issue Number	3
e-ISSN	15597067
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-07-06
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Forward-backward stochastic differential equations Four Step Scheme parabolic integropartial differential equation strong Markov semi-martingales Statistics Statistical Physics, Dynamical Systems and Complexity Mathematics of Computing Operations Research/Decision Theory Systems Theory, Control
Content Type	Text
Resource Type	Article
Subject	Information Systems

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