On the orthogonal component of BSDEs in a Markovian setting

Réveillac, Anthony

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

Number

Publisher

Elsevier

Pages

151-157

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