Pathwise versions of the Burkholder–Davis–Gundy inequality

Mathias Beiglböck; Pietro Siorpaes

doi:10.3150/13-BEJ570

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Home > Journals > Bernoulli > Volume 21 > Issue 1 > Article

February 2015 Pathwise versions of the Burkholder–Davis–Gundy inequality

Mathias Beiglböck, Pietro Siorpaes

Bernoulli 21(1): 360-373 (February 2015). DOI: 10.3150/13-BEJ570

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Abstract

We present a new proof of the Burkholder–Davis–Gundy inequalities for $1\leq p<\infty$. 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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Mathias Beiglböck. Pietro Siorpaes. "Pathwise versions of the Burkholder–Davis–Gundy inequality." Bernoulli 21 (1) 360 - 373, February 2015. https://doi.org/10.3150/13-BEJ570