EXISTENCE AND UNIQUENESS FOR NON-MARKOVIAN TRIANGULAR BSDES

We prove the existence and uniqueness of solutions to a class of quadratic backward results about diagonally quadratic BSDEs in the non-Markovian setting. As part of our analysis, we obtain new results about linear BSDEs with unbounded coefficients, which may be of independent interest. Through a nonuniqueness example, we answer a ``crucial open question"" raised by Harter and Richou by showing that the stochastic exponential of an n \times n matrix-valued bounded mean oscillation martingale need not satisfy a reverse Ho"\lder inequality.