On the orthogonal component of BSDEs in a Markovian setting

Abstract: In this note we consider a quadratic growth backward stochastic differential equation (BSDE) driven by a continuous martingale . We prove (in ) that if is a strong Markov process and if the BSDE has the form with regular data then the unique solution of the BSDE is reduced to , i.e. the orthogonal martingale is equal to zero, showing that in a Markovian setting the “usual” solution (of a BSDE with regular data) has not to be completed by a strongly orthogonal component even if does not enjoy the martingale representation property. [Copyright &y& Elsevier]