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On the orthogonal component of BSDEs in a Markovian setting

Réveillac, Anthony (2012), On the orthogonal component of BSDEs in a Markovian setting, Statistics & Probability Letters, 82, 1, p. 151-157. http://dx.doi.org/10.1016/j.spl.2011.09.015

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00635484/fr/
Date
2012
Journal name
Statistics & Probability Letters
Volume
82
Number
1
Publisher
Elsevier
Pages
151-157
Publication identifier
Metadata
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Author(s)
Réveillac, Anthony
Abstract (EN)
In this note we consider a quadratic growth backward stochastic differential equation (BSDE) driven by a continuous martingale M. We prove (in Theorem 3.2) that if M is a strong Markov process and if the BSDE has the form (2.2) with regular data then the unique solution (Y,Z,N) of the BSDE is reduced to (Y,Z), i.e. the orthogonal martingale N is equal to zero, showing that in a Markovian setting the "usual" solution (Y,Z) (of a BSDE with regular data) has not to be completed by a strongly orthogonal component even if M does not enjoy the martingale representation property.
Subjects / Keywords
Quadratic growth BSDEs; Martingale representation property; Markov processes