Existence and uniqueness for non-Markovian triangular quadratic BSDEs

Abstract: We prove the existence and uniqueness of solutions to a class of quadratic BSDE systems which we call triangular quadratic. Our results generalize several existing 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 non-uniqueness example, we answer a "crucial open question" raised by Harter and Richou by showing that the stochastic exponential of an n x n matrix-valued BMO martingale need not satisfy a reverse H\"older inequality.