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Classical and Variational Differentiability of BSDEs with Quadratic Growth

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Classical and Variational Differentiability of BSDEs with Quadratic Growth
2.	Creator	Author's name, affiliation, country	Stefan Ankirchner; Humboldt Uiversitaet Berlin
2.	Creator	Author's name, affiliation, country	Peter Imkeller; Humboldt Uiversitaet Berlin
2.	Creator	Author's name, affiliation, country	Goncalo JN Dos Reis; Humboldt Uiversitaet Berlin
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	BSDE, forward-backward SDE, quadratic growth, differentiability, stochastic calculus of variations, Malliavin calculus, Feynman-Kac formula, BMO martingale, reverse Holder inequality
3.	Subject	Subject classification	2000 AMS subject classifications: Primary: 60H10; Secondary: 60H07, 65C30
4.	Description	Abstract	We consider Backward Stochastic Differential Equations (BSDEs) with generators that grow quadratically in the control variable. In a more abstract setting, we first allow both the terminal condition and the generator to depend on a vector parameter $x$. We give sufficient conditions for the solution pair of the BSDE to be differentiable in $x$. These results can be applied to systems of forward-backward SDE. If the terminal condition of the BSDE is given by a sufficiently smooth function of the terminal value of a forward SDE, then its solution pair is differentiable with respect to the initial vector of the forward equation. Finally we prove sufficient conditions for solutions of quadratic BSDEs to be differentiable in the variational sense (Malliavin differentiable).
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	DFG Research Center MATHEON
7.	Date	(YYYY-MM-DD)	2007-11-09
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/462
10.	Identifier	Digital Object Identifier	10.1214/EJP.v12-462
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 12
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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