The reverse Hölder inequality for matrix-valued stochastic exponentials and applications to quadratic BSDE systems

Joe Jackson

Stochastic Processes and their Applications, 2023, vol. 160, issue C, 1-32

Abstract: In this paper, we study the connections between three concepts — the reverse Hölder 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 coefficients is well-posed if and only if the stochastic exponential of a related matrix-valued martingale satisfies a reverse Hölder inequality. Furthermore, we give structural conditions under which these 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.

Date: 2023
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DOI: 10.1016/j.spa.2023.02.011

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