The reverse H\"older inequality for matrix-valued stochastic exponentials and applications to quadratic BSDE systems
Probability
2022-03-01 v1
Abstract
In this paper, we study the connections between three concepts - the reverse H\"older inequality for matrix-valued martingales, the well-posedness of linear BSDEs with unbounded coefficients, and the well-posedness of quadratic BSDE systems. In particular, we show that a linear BSDE with bmo (bounded mean oscillation) coefficients is well-posed if and only if the stochastic exponential of a related matrix-valued martingale satisfies a reverse H\"older inequality. Furthermore, we give structural conditions under which these two equivalent conditions are satisfied. Finally, we apply our results on linear equations to obtain global well-posedness results for two new classes of non-Markovian quadratic BSDE systems with special structure.
Keywords
Cite
@article{arxiv.2202.13886,
title = {The reverse H\"older inequality for matrix-valued stochastic exponentials and applications to quadratic BSDE systems},
author = {Joe Jackson},
journal= {arXiv preprint arXiv:2202.13886},
year = {2022}
}