Pathwise versions of the Burkholder-Davis-Gundy inequality
Mathias Beiglb\"ock, Pietro Siorpaes
TL;DR
This paper introduces a new proof of the Burkholder-Davis-Gundy inequalities for martingales, deriving them from elementary deterministic inequalities with interpretations in robust hedging, offering a novel perspective on these fundamental results.
Contribution
It provides a new proof method for the inequalities using deterministic counterparts, connecting martingale inequalities with robust hedging strategies.
Findings
New proof of Burkholder-Davis-Gundy inequalities
Elementary deterministic inequalities imply martingale inequalities
Interpretation in terms of robust hedging
Abstract
We present a new proof of the Burkholder-Davis-Gundy inequalities for . The novelty of our method is that these martingale inequalities are obtained as consequences of elementary deterministic counterparts. The latter have a natural interpretation in terms of robust hedging.
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