On the orthogonal component of BSDEs in a Markovian setting

Anthony Réveillac

Statistics & Probability Letters, 2012, vol. 82, issue 1, 151-157

Abstract: In this note we consider a quadratic growth backward stochastic differential equation (BSDE) driven by a continuous martingale M. We prove (in ) that if M is a strong Markov process and if the BSDE has the form 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.

Keywords: Quadratic growth BSDEs; Martingale representation property; Markov processes (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.09.015

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